Inverse of a Rational Function (2)
Finding the inverse of a rational function and its domain
tags:
Domain Function Horizontal Line Test How-To Precalculus Inverse Function One-to-one Rational FunctionInverse of a Rational Function
Author: Doan Nguyen
The following problem is solved in this video. It is recommended that you try to solve the problem before watching the video. You can click "Reveal Answer" to reveal the answer to the problem.
Problem: Find the inverse of the following function and its domain:\[
f(x) = \frac{1}{2-x}
\]
\(f^{-1}(x)=2-\dfrac{1}{x}\)
Domain of \( f^{-1}(x)\): \((-\infty,0)\cup(0,\infty)\)
Domain of \( f^{-1}(x)\): \((-\infty,0)\cup(0,\infty)\)
See more videos from this section
Related Videos
Inverse of a Linear Function
Finding the inverse of a linear function and its domain
Inverse of a Square Root Function
Finding the inverse of a square root function and its domain
WIR3 20B M150 V20
Restricting the domain of a function so it is one-to-one and has an inverse
WIR3 20B M150 V21
Determining algebraically the inverse of a function
WIR3 20B M150 V22
Determining algebraically the inverse of a function
WIR3 20B M150 V23
Determining algebraically the inverse of a function
Inverse Trigonometric Functions: MATH 151 1.5 Problems 9-12
Properties and derivatives of inverse trigonometric functions
Inverse Trigonometric Functions: MATH 151 Problems 9-12
Properties and derivatives of inverse trigonometric functions
Inverse Trigonometric Functions: MATH 151 1.5 Problems 9-12
Properties and derivatives of inverse trigonometric functions
Inverse Trigonometric Functions: MATH 151 Problems 9-12
Properties and derivatives of inverse trigonometric functions
WIR8 20B M150 V03
Finding the domains of expressions
Inverse Trigonometric Functions: MATH 171 Problems 4-6
Properties of inverse trig functions and the derivative of arctangent
Domain of a Rational Function
Finding the domain of a rational function
Domain of a Rational Function (2)
Finding the domain of a rational function
Function Composition with a Rational Function
Finding the composition of a rational function and a quadratic
MATH 140 5.1 Exercise 2
Determining the domain and range of a relation and if the relation is a function
MATH 140 5.1 Exercise 3
Determining the domain and range of a relation and if the relation is a function
MATH 140 5.1 Exercise 4
Determining the domain and range of a relation and if the relation is a function
MATH 140 5.5 Exercise 1
Finding the domain of a piecewise function and evaluating it
MATH 140 5.8 Exercise 3
Using the Horizontal Line Test to determine if graphs represent invertible functions
MATH 140 5.3 Exercise 1
Finding the domain, intercepts, asymptotes, and holes of a rational function
MATH 140 5.3 Exercise 2
Finding the domain, intercepts, asymptotes, and holes of a rational function
MATH 140 5.3 Exercise 3
Finding the domain, intercepts, asymptotes, and holes of a rational function
Absolute Extrema on a Closed Interval
Finding the absolute maximum and minimum of a rational function on two closed intervals
WIR2 20B M150 V10
Finding the domains of functions
WIR3 20B M150 V13
Determining the properties of a rational function and graphing it
WIR8 20B M150 V09
Determining the properties of a rational function and graphing it
WIR3 20B M150 V19
Graphically verifying if two functions are inverses
WIR4 20B M150 V1
Determining properties of an exponential function
WIR4 20B M150 V2
Determining properties of an exponential function
WIR4 20B M150 V3
Determining properties of an exponential function
WIR4 20B M150 V4
Identifying the graph of an exponential function
WIR8 20B M150 V10
Determining properties of an exponential function
WIR2 20B M150 V11
Using a graph to evaluate a function
Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15
Review of limits and derivatives of inverse trigonometric functions
Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15
Review of limits and derivatives of inverse trigonometric functions
Continuity: MATH 151 2.5 Problems 1-6
Continuity of Functions and the Intermediate Value Theorem
Studying the Shape of Curves: MATH 151 4.1 Problems 2-7
Using derivatives to find properties of graphs
Studying the Shape of Curves: MATH 151 Problems 2-7
Using derivatives to find properties of graphs
Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15
Review of limits and derivatives of inverse trigonometric functions
Continuity: MATH 151 2.5 Problems 1-6
Continuity of Functions and the Intermediate Value Theorem
Studying the Shape of Curves: MATH 151 4.1 Problems 2-7
Using derivatives to find properties of graphs
Studying the Shape of Curves: MATH 151 Problems 2-7
Using derivatives to find properties of graphs
WIR2 20B M251 V6
Determining the domain of a three-dimensional vector function
WIR2 20B M150 V7
Solving a rational equation and checking the solutions
Math 140 Exam 3 Review Exercise 5
Finding the domain, intercepts, holes, and vertical asymptotes for a rational function
Math 140 Exam 3 Review Exercise 1
Determining if a graph represents a function and finding the domain and range
Simplifying a Rational Expression
Simplifying a rational expression
Subtracting Rational Expressions
Adding and then simplifying two rational expressions
Multiplying Rational Expressions
Multiplying two rational expressions and then simplifying
Dividing Rational Expressions
Dividing rational expressions and then simplifying the answer
Adding Rational Expressions
Adding two rational expressions and then simplifying the answer
Holes and Asymptotes of Rational Functions
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Holes and Asymptotes of Rational Functions (2)
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Matching a Rational Function with its Graph
Matching a rational function with its graph
Domain of Function with Roots
Finding the domain of a function with a fraction and radicals
Domain of a Square Root Function
Finding the domain of a function with a quadratic inside a square root
Composition of Polynomial Functions
Finding the composition of two functions
Composition of Logarithmic and Exponential Functions
Finding the composition of two functions with exponentials and logarithms
Composition of Square Root and Power Functions
Finding the composition of two functions with a square root and a fractional exponent
Composition of Cube Root and Power Functions
Finding the composition of two functions with a cube root and a fractional exponent
Difference Quotient of a Rational Function
Finding and simplifying the difference quotient for a rational function
Difference Quotient of a Square Root Function
Finding and simplifying the difference quotient for a square root function
Solving an Inequality with a Rational Function
Solving an inequality with a rational expression by factoring and using a sign diagram
Solving an Inequality with a Sum of Rational Functions
Solving an inequality with two rational expressions using a sign diagram
Solving an Inequality with by Finding a Least Common Denominator
Solving an inequality with a rational expression using a sign diagram
Domain and x-intercepts of a Logarithmic Function
Finding the domain and x-intercepts of a logarithmic function
Domain and x-intercepts of a Logarithmic Function (2)
Finding the domain and x-intercepts of a logarithmic function
Solving an Equation with Logarithms
Solving a logarithmic equation using properties of logarithms
Solving an Equation with a Logarithmic Function
Solving a logarithmic equation using properties of logarithms
Domain Restrictions
Explaining domain restrictions for denominators, even roots, and logarithms
Domain of Rational Functions Video 1
Finding the domain of several rational functions
Domain of Rational Functions Video 2
Finding the domain of a rational function
Domain of Rational Functions Video 3
Explaining how to find any holes and vertical asymptotes of a rational function
Domain of Rational Functions Video 4
Finding the domain of a rational function using factoring
Domain of Combinations of Functions Video 1
Finding the domain of a function with a denominator, square root, and logarithm
Properties of Rational Functions and Expressions Video 1
Discussing parent functions of rational functions and their properties
Properties of Rational Functions and Expressions Video 9
Explaining how to multiply and divide rational expressions
Properties of Rational Functions and Expressions Video 10
Performing algebraic operations with rational expressions and simplifying the answer
Solving Rational Equations Video 1
Solving equations that contain rational expressions
Solving Rational Equations Video 2
Solving an equation that contains rational expressions
Solving Rational Equations Video 3
Solving an equation that contains rational expressions
Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15
Review of limits and derivatives of inverse trigonometric functions
MATH 140 5.1 Exercise 5
Using a graph to find specific values of a function
MATH 140 5.1 Exercise 6
Finding function values and expressions given the rule or equation of the function
MATH 140 5.2 Exercise 1
Determining if functions are polynomials and finding their properties
MATH 140 5.2 Exercise 2
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
MATH 140 5.2 Exercise 3
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
MATH 140 5.2 Exercise 4
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
MATH 140 5.2 Exercise 5
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
MATH 140 5.2 Exercise 6
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
MATH 140 5.5 Exercise 2
Finding the piecewise-defined function for a given graph along with its domain and range
MATH 140 5.6 Exercise 1
Finding the properties of an exponential function including domain, range, end behavior, and intercepts
MATH 140 5.6 Exercise 2
Finding the properties of an exponential function including domain, range, end behavior, and intercepts
MATH 140 5.6 Exercise 3
Finding the properties of an exponential function including domain, range, end behavior, and intercepts
MATH 140 5.6 Exercise 4
Finding the domain of a function that is a fraction containing an exponential and root
MATH 140 5.6 Exercise 5
Finding the domain of a function that is a fraction containing an exponential and root
MATH 140 5.6 Exercise 6
Finding the domain of a function that is a fraction containing exponentials and a square root
MATH 140 5.8 Exercise 10
Finding the domain of a function containing several logarithms
MATH 140 5.8 Exercise 11
Finding the domain of a function containing a logarithm, exponential, and fraction
MATH 140 5.8 Exercise 4
Evaluating a logarithm inside an exponential function
MATH 140 5.8 Exercise 7
Finding the domain, range, end behavior, and intercepts for a logarithmic function
MATH 140 5.8 Exercise 9
Finding the domain of a function containing a logarithm, exponential, radical, and fraction
MATH 140 5.3 Exercise 4
Adding and simplifying rational functions
MATH 140 5.3 Exercise 5
Subtracting rational functions and then simplifying the result
MATH 140 5.3 Exercise 6
Multiplying two rational functions and simplifying the result
MATH 140 5.3 Exercise 7
Dividing rational functions and simplifying the result
MATH 140 5.3 Exercise 8
Dividing and subtraction rational functions and simplifying the result
MATH 140 5.3 Exercise 9
Computing and simplifying the difference quotient for a rational function
Limit of a Rational Function
Finding the limit of a rational function algebraically
Limit of a Rational Function 2
Finding the limit of a rational function algebraically
Limit at Negative Infinity of a Rational Function
Solving a limit approaching negative infinity for a rational function
Limits at Infinity of a Rational Function
Solving the limits approaching infinity and negative infinity of a rational function
Limits at Infinity of a Rational Function 2
Solving the limits approaching infinity and negative infinity of a rational function
Vertical Asymptotes and Holes of a Rational Function
Finding the holes and vertical asymptotes of a rational function
Instantaneous Rate of Change of a Rational Function
Finding the exact value of the instantaneous rate of change
Finding the Derivative of a Rational Function Using the Limit Definition
Using the limit definition to find the derivative of a rational function
Finding a Derivative by Simplifying a Rational
Finding the derivative of a rational function by simplifying and using the power rule
Using the Quotient Rule on a Rational Function
Finding the derivative of a rational function using the Quotient Rule
Finding Where a Function is Increasing and Decreasing
Determining the intervals where a function is increasing and decreasing
Increasing and Decreasing and Local Extrema
Finding the intervals where a function is increasing/decreasing and the local extrema
Increasing and Decreasing and Local Extrema for a Revenue Function
Finding intervals of increase/decrease and the local extema for revenue from a word problem
Using the Quotient Rule Twice to Find the Second Derivative
Using the quotient rule twice to find the second derivative of a rational function
Inflection Points and Intervals of Concavity for an Exponential Function
Finding the intervals of concavity and inflection points for a function with exponentials
Inflection Points and Intervals of Concavity from a Graph
Determining the intervals of concavity and inflection points from the graph of a function
Using the Second Derivative Test to Find Local Extrema
Using the second derivative test to find local extrema for a function
Absolute Extrema on a Closed Interval 2
Finding the absolute maximum and absolute minimum of a rational function on two closed intervals
Finding the Price to Maximize Profit
Finding the selling price of trucks to maximize profit given the cost and price-demand functions
Finding the Box with the Largest Volume
Finding the dimensions of the box with the largest volume given the amount of material to make the box
Minimizing the Cost of a Box
Finding the minimum cost of a box given the volume and cost of materials
Calculating the Exact Area Under a Curve With Geometry
Using geometric formulas for circles, triangles, and rectangles to find the exact area under a curve
WIR7 20B M150 V13
Calculating the difference quotient for a rational function
WIR8 20B M150 V15
Calculating the difference quotient for a rational function
WIR1 20B M150 V16
Dividing rational expressions and simplifying
WIR1 20B M150 V17
Subtracting rational expressions and simplifying
WIR1 20B M150 V18
Performing operations with rational expressions and simplifying
WIR8 20B M150 V04
Performing operations with rational expressions and simplifying
WIR2 20B M150 V8
Determining if an equation represents a function
WIR2 20B M150 V9
Evaluating a piecewise function
WIR2 20B M150 V13
Identifying the parent function and transformations of a function
WIR2 20B M150 V14
Identifying the parent function and transformations of a function
WIR3 20B M150 V18
Finding combinations of functions and their domains
WIR4 20B M150 V7
Determining the properties of a logarithmic function
WIR4 20B M150 V8
Determining the graph of a logarithmic function
WIR4 20B M150 V9
Determining the properties of a logarithmic function
WIR4 20B M150 V10
Determining the graph of a logarithmic function
WIR4 20B M150 V19
Solving an equation with an exponential function
WIR4 20B M150 V20
Solving an equation with exponential functions by factoring
WIR2 20B M150 V12
Determining if a function is even or odd
Parametric Curves: MATH 151 J.3 Problems 1-5
Cartesian equations and parametric equations of curves
Vectors and Derivatives: MATH 151 K.1 Problems 1-8
Derivatives and vectors with some physics applications
Review for the Common Exam: MATH 151 Exam 1 Review Problems 14-25
Review of limits, continuity, and the Intermediate Value Theorem
Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Review for the Common Exam: MATH 151 Exam 2 Review Problems 21-29
Related rates problems, differentials, linear and quadratic approximations
Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Review for Common Exam: MATH 151 Exam 3 Review Problems 15-19
Mean Value Theorem and using derivatives to find the shape of curves
Limits: MATH 151 Problems 6-20
Evaluating limits of functions
Limits: MATH 151 Problems 6-20
Evaluating Limits of Functions
Limits and Asymptotes: MATH 151 2.6 Problems 7-11
Limits at infinity and asymptotes, along with physics applications
Limits and Asymptotes: MATH 151 2.7 Problems 7-11
Limits at infinity, asymptotes, and tangent lines
Review for the Common Exam: MATH 151 3.1 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Differentials and Approximations: MATH 151 3.10 Problems 1-6
Differentials, linear approximations and quadratic approximations
Review for the Common Exam: MATH 151 3.2 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Vectors and Derivatives: MATH 151 3.4 Problems 1-8
Derivatives and vectors with some physics applications
Differentiation and Applications: MATH 151 Problems 1-8
Derivatives of exponential and logarithmic functions and the exponential model
Vectors and Derivatives: MATH 151 3.7 Problems 1-8
Derivatives and vectors with some physics applications
Differentiation and Applications: MATH 151 3.8 Problems 1-8
Derivatives of exponential and logarithmic functions and the exponential model
Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.2 Problems 1-6
Mean Value Theorem and properties of a graph
Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.3 Problems 1-6
Mean Value Theorem and properties of a graph
Riemann Sums and Definite Integrals: MATH 151 5.2 Problems 6-12
Using Reimann sums and the Fundamental Theorem of Calculus
Riemann Sums and Definite Integrals: MATH 151 5.3 Problems 6-12
Using Riemann sums and the Fundamental Theorem of Calculus
Integration by Substitution: MATH 151 5.5 Problems 13 & 14
Examples of integration by substitution
MLC WIR 20B M151 week3 #16
Finding the vertical and horizontal asymptotes for a rational function
MLC WIR 20B M151 week4 #1h
Using the Quotient Rule to differentiate a rational function
MLC WIR 20B M151 week7 #4a
Evaluating a limit using L'Hospital's Rule
MLC WIR 20B M151 week9 #8a
Evaluating a limit using logarithm properties
MLC WIR 20B M151 week9 #8b
Evaluating a limit with an indeterminate difference using a common denominator
MLC WIR 20B M151 week9 #10b
Finding the antiderivative of a rational function
MLC WIR 20B M151 week10 #6a
Evaluating a a limit from the left for a rational function
MLC WIR 20B M151 week10 #6b
Evaluating the limit of a rational function by factoring and cancelling
MLC WIR 20B M151 week10 #6c
Using L'Hospital's Rule to evaluate a limit representing a derivative at a point
MLC WIR 20B M151 week10 #8a
Evaluating the limit at infinity of a rational function
MLC WIR 20B M151 week10 #24b
Evaluating a definite integral by first simplifying the integrand
Review for the Common Exam: MATH 152 Exam 1 a Review Problems 1-4
Reviewing u-Substitution
Review for the Common Exam: MATH 152 Exam 1 b Review Problem 36
Review of partial fractions
Review for the Common Exam: MATH 152 Exam 1 b Review Problems 34 & 35
Review of partial fractions
WIR 20B M152 V2
Integrating a rational function using u-substitution
WIR 20B M152 V3
Integrating a rational function using u-substitution
MATH 152: u-Substitution Exercise 3
Using u-substitution to integrate a rational function
Cases for Partial Fraction Decomposition
Explaining all four cases of partial fraction decomposition
MATH 152: Partial Fraction Decomposition Exercise 1
Using partial fraction decomposition to rewrite and then integrate a rational function
MATH 152: Partial Fraction Decomposition Exercise 2
Using partial fraction decomposition to rewrite and then integrate a rational function
MATH 152: Partial Fraction Decomposition Exercise 3
Using partial fraction decomposition to rewrite and then integrate a rational function
MATH 152: Partial Fraction Decomposition Exercise 5
Using partial fraction decomposition to rewrite and then integrate a rational function
MATH 152: Partial Fraction Decomposition Exercise 6
Using partial fraction decomposition to rewrite and then integrate a rational function
Vector Functions: MATH 171 Problems 1 & 2
Proving a certain parameterization gives the unit circle and showing vector equations of lines are parallel
Parametric Curves: MATH 151 J.3 Problems 1-5
Cartesian equations and parametric equations of curves
Vectors and Derivatives: MATH 151 K.1 Problems 1-8
Derivatives and vectors with some physics applications
Review for the Common Exam: MATH 151 Exam 2 Review Problems 21-29
Related rates problems, differentials, linear and quadratic approximations
Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Review for Common Exam: MATH 151 Exam 3 Review Problems 15-19
Mean Value Theorem and using derivatives to find the shape of curves
Limits: MATH 151 Problems 6-20
Evaluating limits of functions
Limits: MATH 151 Problems 6-20
Evaluating Limits of Functions
Continuity: MATH 171 Problems 6 & 7
Proving a piecewise function and a polynomial are continuous
Limits and Asymptotes: MATH 151 2.6 Problems 7-11
Limits at infinity and asymptotes, along with physics applications
Limits and Asymptotes: MATH 151 2.7 Problems 7-11
Limits at infinity, asymptotes, and tangent lines
Derivatives and Rates of Change: MATH 171 Problems 1-3
Using the limit definition to find derivatives of functions and vector functions
Review for the Common Exam: MATH 151 3.1 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Differentials and Approximations: MATH 151 3.10 Problems 1-6
Differentials, linear approximations and quadratic approximations
Review for the Common Exam: MATH 151 3.2 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Higher Order Derivatives: MATH 171 Problems 4-6
Finding a formula for a higher order derivative and a formula for the second derivative of a product
Vectors and Derivatives: MATH 151 3.4 Problems 1-8
Derivatives and vectors with some physics applications
Derivatives of Logarithmic Functions: MATH 171 Problems 7-9
Proving facts about logarithms and exponentials including the derivative of an exponential with an arbitrary base
Differentiation and Applications: MATH 151 Problems 1-8
Derivatives of exponential and logarithmic functions and the exponential model
Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.2 Problems 1-6
Mean Value Theorem and properties of a graph
Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.3 Problems 1-6
Mean Value Theorem and properties of a graph
Riemann Sums and Definite Integrals: MATH 151 5.2 Problems 6-12
Using Reimann sums and the Fundamental Theorem of Calculus
Riemann Sums and Definite Integrals: MATH 151 5.3 Problems 6-12
Using Riemann sums and the Fundamental Theorem of Calculus
Integration by Substitution: MATH 151 5.5 Problems 13 & 14
Examples of integration by substitution
Review for the Common Exam: MATH 152 Exam 1 a Review Problems 1-4
Reviewing u-Substitution
Review for the Common Exam: MATH 152 Exam 1 b Review Problem 36
Review of partial fractions
Review for the Common Exam: MATH 152 Exam 1 b Review Problems 34 & 35
Review of partial fractions
Work and Average Value: MATH 152 Problems 1-9
Using integrals to solve work problems and find the average value
Integration Using Partial Fractions: MATH 172 Problems 8 & 9
Finding a partial fraction decomposition and integrating using partial fractions
Cases for Partial Fraction Decomposition
Explaining all four cases of partial fraction decomposition
WIR2 20B M251 V7
Finding the limit of a three-dimensional vector function
WIR3 20B M251 V1
Finding and sketching the domain of a function of two variables
WIR3 20B M251 V2
Finding and sketching the domain of a function of two variables
Functions of Several Variables Exercise V1
Evaluating and then finding and sketching the domain of a function of two variables
Functions of Several Variables Exercise V2
Finding and sketching the domain of a function of two variables
Functions of Several Variables Exercise V4
Sketching the level curves for a function of two variables
Functions of Several Variables Exercise V5
Sketching the level curves for a function of two variables
Cases for Partial Fraction Decomposition
Explaining all four cases of partial fraction decomposition
Math 140 5.4 Exercise 4
Writing the domain of functions with radicals in interval notation
WIR4 20B M150 V21
Solving an equation with logarithmic functions
WIR4 20B M150 V22
Solving an equation with logarithmic functions
WIR4 20B M150 V23
Solving an equation with logarithmic functions
WIR4 20B M150 V24
Solving an equation with logarithmic functions
WIR8 20B M150 V11
Solving an equation with logarithmic functions
Math 140 Exam 3 Review Exercise 7
Compute and simplify the difference quotient for a rational function
Math 140 Exam 3 Review Exercise 9
Finding the domain of a piecewise-defined function and evaluating it for given x-values
Math 140 Exam 3 Review Exercise 10
Finding properties of a polynomial function such as the degree, end behavior, y-intercept, etc.
Math 140 Exam 3 Review Exercise 11
Finding properties of a polynomial function such as the degree, end behavior, y-intercept, etc.
Math 140 Exam 3 Review Exercise 13
Stating the domain in interval notation of a function with radicals, fractions, and exponentials
Math 140 Exam 3 Review Exercise 24
Find the domain of a function in interval notation with a fraction and logarithm
Math 140 Exam 3 Review Exercise 2
test
Math 140 Exam 3 Review Exercise 4
Finding the properties of a quadratic function such as the vertex, axis of symmetry, intercepts, etc.
Equation of a Line Given Two Points
Writing the equation of a line passing through two points
Slope-Intercept Form of an Equation for a Line
Writing the equation of a line through two points in slope-intercept form
Standard Form of an Equation for a Line
Writing the equation of a graphed line in standard form
Factoring a Quadratic
Factoring a quadratic polynomial
Factoring a Quadratic (2)
Factoring a quadratic function
Factoring by Grouping
Factoring a cubic polynomial by grouping
Factoring Out the Greatest Common Factor
Finding the greatest common factor of a polynomial and then factoring it out
Factoring a Quadratic: Leading Coefficient is 1
Factoring a quadratic where the leading coefficient is 1
Factoring a Quadratic: Leading Coefficient is Not 1
Factoring quadratics where the leading coefficient is not 1
Factoring by Grouping (2)
Factoring several polynomials by grouping
Factoring a Difference of Two Squares
Factoring a difference of two squares
Factoring a Sum and Difference of Cubes
Factoring a sum of cubes and a difference of cubes
Roots of a Quadratic
Using the quadratic formula to find the roots of a function
Roots of a Polynomial
Finding the roots of a cubic polynomial
Roots of a Square Root Function
Finding the roots of a square root function
Roots of a Function with an Absolute Value
Finding the roots of a function with an absolute value
Difference Quotient of a Quadratic
Finding and simplifying the difference quotient for a quadratic function
Solving an Inequality with a Polynomial
Solving an inequality with a polynomial by factoring and using a sign diagram
Solving an Inequality with a Quadratic Function
Solving an inequality with a quadratic by factoring and using a sign diagram
Absolute Maximum or Minimum of a Quadratic
Finding the absolute maximum or absolute minimum of a quadratic
Standard Form of a Quadratic
Writing the standard form of quadratic function given its vertex and one other point
Component Form and Magnitude of a Vector
Finding the component form and magnitude for a vector between two points
Vector Addition and Subtraction and Scalar Multiplication
Performing calculations with vectors including addition, subtraction, and scalar multiplication
Dot Product
Calculating the dot product for three pairs of vectors
Finding a Unit Vector
Finding a unit vector in the direction of a given vector
Solving a System of Equations
Solving a system of two linear equations using the method of substitution
Solving a System of Equations (2)
Solving a system of two linear equations using the method of substitution
Solving a System of Equations (3)
Solving a system of two linear equations
Solving a System of Nonlinear Equations
Solving a system on two equations where one is linear and one is quadratic
An Equation with an Exponential Function
Solving a equation with an exponential function
An Equation with Exponential Functions of Different Bases
Solving an equation with two exponential functions with different bases
Factoring a Quadratic-Like Equation with Exponentials
Solving an equation with exponential functions by factoring
Factoring an Equation with Exponentials
Solving a equation with exponential functions by factoring
Population Model with Exponential Growth
Finding the size of a population of rabbits with exponential growth
Population Model with Exponential Decay
Finding the size of a population of rabbits with exponential decay
Horizontal Asymptote of an Exponential Function
Finding the horizontal asymptote of an exponential function
Horizontal Asymptote of an Exponential Function (2)
Finding the horizontal asymptote of an exponential function
Horizontal Asymptote of an Exponential Function (3)
Finding the horizontal asymptote of an exponential function
Expanding a Logarithmic Expression
Expanding a logarithmic expression using logarithm properties
Condensing a Logarithmic Expression
Condensing logarithmic expressions into a single logarithm
Evaluating Logarithmic Expressions
Finding the exact value of logarithms using logarithmic properties
Vertical Asymptote of a Logarithmic Function
Finding the vertical asymptote of a logarithmic function
Vertical Asymptote of a Logarithmic Function (2)
Finding the vertical asymptote of a logarithmic function
Evaluating All Six Trigonometric Functions
Finding the values of all six trigonometric functions of an angle given a right triangle
Evaluating the Other Trigonometric Functions Given Sine
Evaluating the other five trigonometric functions for an acute angle given the value of sine
Evaluating the Other Trigonometric Functions Given Sine (2)
Evaluating the other five trigonometric functions given sine and that tangent is negative
Solving an Equation with Tangent
Finding the solutions to an equation with tangent in a given interval
Solving an Equation with Sine and Cosine
Solving a trigonometric equation with sine and cosine on a given interval
Factoring a Quadratic-Like Equation with Sine
Solving an quadratic-like equation with sine by factoring
Solving an Equation with Cosine
Solving an equation with cosine on a given interval
Solving an Equation with Sine
Solving a trigonometric equation with sine on a given interval
Sketching One Period of a Sine Function
Sketching one period of a transformed sine graph
Sketching One Period of a Cosine Function
Sketching one period of a cosine function with transformations
Properties of a Sine Function
Finding the amplitude, period, phase shift, and vertical shift for a given sine function
Find the Cosine Function for a Graph
Writing a cosine function for a given graph
Creating and Manipulating Symbolic Expressions in Python
Creating symbolic expression in Python and then factoring, expanding, and simplifying the expressions
Domain of Radical Functions Video 1
Finding the domain of even and odd roots
Domain of Radical Functions Video 2
Finding the domain of functions with even and odd roots
Domain of Logarithmic Functions Video 1
Finding the domain of a logarithmic function
Domain of Combinations of Functions Video 2
Finding the domain of a function with a natural logarithm and denominator
Domain of Combinations of Functions Video 4
Finding the domain of a function with a root and a logarithm in the denominator
Linear Forms Video 2
Discussing properties of linear functions
Linear Graphs Video 1
Discussing the types of linear graphs including horizontal and vertical lines and their properties
Quadratic Form Video 1
Explaining the graph and properties for the parent function of quadratics
Quadratic Form Video 2
Discussing properties of quadratic functions including the vertex, domain, range, and end behavior
Properties of Rational Functions and Expressions Video 2
Finding horizontal asymptotes for rational functions
Properties of Rational Functions and Expressions Video 4
Finding horizontal asymptotes for rational functions
Properties of Rational Functions and Expressions Video 5
Determining the end behavior and horizontal asymptotes for rational functions
Properties of Rational Functions and Expressions Video 7
How to simplify rational expressions
Properties of Rational Functions and Expressions Video 8
Adding and subtracting rational expressions by finding a common denominator
Properties of Rational Functions and Expressions Video 3
Explaining how to do polynomial long division
Properties of Radical Functions and Expressions Video 1
Explaining the general properties of even and odd root functions
Solving Radical Equations Video 1
Explaining how to solve radical equations and then solving example problems
Solving Radical Equations Video 2
Solving equations with even roots and checking the solutions
Solving Radical Equations Video 3
Solving equations with odd radicals
Solving Radical Equations Video 4
Solving equations with multiple radicals
Properties of Power and Exponential Expressions Video 4
Properties of exponential growth and decay functions
Properties of Power and Exponential Expressions Video 5
Properties of the exponential function with base e
Solving Power and Exponential Equations Video 1
Explaining how to solve equations with power and exponential terms
Properties of Logarithmic Functions and Expressions Video 2
Explaining the basic properties of logarithmic functions
Properties of Logarithmic Functions and Expressions Video 3
Expanding logarithmic expressions using logarithm rules
Properties of Logarithmic Functions and Expressions Video 4
Condensing a logarithmic expression into a single logarithm
Solving Logarithmic Equations Video 1
Explaining how to solve logarithmic equations
Solving Logarithmic Equations Video 2
Solving logarithmic equations with a single logarithm term
Solving Logarithmic Equations Video 3
Solving logarithmic equations with multiple logarithm terms
Solving Logarithmic Equations Video 4
Solving logarithmic equations with multiple logarithm terms on both sides
Splitting a Domain Into Two Pieces for a Double Integral
Evaluating a double integral over a given region by splitting it into two double integrals
Linear Forms Video 2
Discussing properties of linear functions
Linear Graphs Video 1
Discussing the types of linear graphs including horizontal and vertical lines and their properties
Properties of Power and Exponential Expressions Video 4
Properties of exponential growth and decay functions
Properties of Power and Exponential Expressions Video 5
Properties of the exponential function with base e
Properties of Logarithmic Functions and Expressions Video 2
Explaining the basic properties of logarithmic functions
Review for the Common Exam: MATH 151 Exam 1 Review Problems 14-25
Review of limits, continuity, and the Intermediate Value Theorem
Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative