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How To ... Precalculus

Recommended Level: MATH 150

Algebra, Functions, Linear Systems, Vectors, and Trigonometry

The following How To videos explain topics you will see in precalculus, including algebra techniques, functions, the difference quotient, vectors, systems of equations, exponentials, logarithms, and trigonometry. These videos cover the topics in MATH 150, but are also a helpful refresher of precalculus topics for students in all MATH courses. 
Video Playlists
Click the playlist you are interested in to go straight to those videos. Or you can scroll down through the page to look through all the videos yourself.
Equations of Lines
3 videos
Equations of Lines
Writing the different forms for the equations of a line given two points on the line
Factoring
3 videos
Factoring
Factoring polynomials
Rational Functions
8 videos
Rational Functions
Performing operations with rational expressions and finding the holes and vertical asymptotes of rational functions
Roots of Functions
4 videos
Roots of Functions
Finding the roots of functions
Functions: Domain, Composition and Inverses
13 videos
Functions: Domain, Composition and Inverses
Finding the domain and inverse of common functions and finding the composition of two functions
Difference Quotient
3 videos
Difference Quotient
Finding the difference quotient and simplifying your answer
Solving Inequalities
5 videos
Solving Inequalities
Using a sign diagram to solve inequalities
Properties of a Quadratic
2 videos
Properties of a Quadratic
Writing a quadratic in standard form and determining its absolute maximum or minimum
Vectors
4 videos
Vectors
Calculating vector operations and the dot product and finding a unit vector
Systems of Equations
5 videos
Systems of Equations
Solving systems of linear equations and systems including a quadratic equation
Exponential Functions
9 videos
Exponential Functions
Solving equations with exponential functions, modeling population size and finding the horizontal asymptote
Logarithmic Functions
9 videos
Logarithmic Functions
Using properties of logarithms, finding the vertical asymptote, and solving equations with logarithmic functions
Trigonometry
13 videos
Trigonometry
Evaluating trigonometric and inverse trigonometric functions, solving trigonometric equations, and graphing trigonometric functions
 
Equations of Lines
These videos show how to write the different forms for the equations of a line given two points on the line.
Equation of a Line Given Two Points
Equation of a Line Given Two Points
Slope-Intercept Form of an Equation for a Line
Slope-Intercept Form of an Equation for a Line
Standard Form of an Equation for a Line
Standard Form of an Equation for a Line
Factoring
These videos show the different methods to factor polynomials.
Factoring a Quadratic
Factoring a Quadratic
Factoring a Quadratic
Factoring a Quadratic (2)
Factoring by Grouping
Factoring by Grouping
Rational Functions
These videos show how to perform operations with rational expressions and find the holes and vertical asymptotes for rational functions.
Operations with Rational Expressions
These videos show how to perform operations with rational expression such as subtraction, multiplication, and division and then simplify the resulting expression.
 
Simplifying a Rational Expression
Simplifying a Rational Expression
Subtracting Rational Expressions
Subtracting Rational Expressions
Multiplying Rational Expressions
Multiplying Rational Expressions
Dividing Rational Expressions
Dividing Rational Expressions
Adding Rational Expressions
Adding Rational Expressions

Holes and Asymptotes of Rational Functions
These videos show how to find the holes and vertical asymptotes of a rational expression and use those properties to identify the graph.
 
Holes and Asymptotes of Rational Functions
Holes and Asymptotes of Rational Functions
Holes and Asymptotes of Rational Functions
Holes and Asymptotes of Rational Functions (2)
Matching a Rational Function with its Graph
Matching a Rational Function with its Graph
Roots of Functions
These videos show how to find the roots of functions. Note exponential, logarithmic, and trigonometric functions are on a different How To page.
Roots of a Quadratic
Roots of a Quadratic
Roots of a Polynomial
Roots of a Polynomial
Roots of a Square Root Function
Roots of a Square Root Function
Roots of a Function with an Absolute Value
Roots of a Function with an Absolute Value
 
Functions: Domain, Composition and Inverses
These videos find the domain, composition, and inverses of common functions. Note exponential, logarithmic, and trigonometric functions are on a different How To page.
Domain of Functions
These videos find the domains of functions that include fractions and roots.
 
Domain of a Rational Function
Domain of a Rational Function
Domain of a Rational Function
Domain of a Rational Function (2)
Domain of Function with Roots
Domain of Function with Roots
Domain of a Square Root Function
Domain of a Square Root Function

Composition of Functions
These videos show how to find the composition of two functions.
 
Composition of Polynomial Functions
Composition of Polynomial Functions
Function Composition with a Rational Function
Function Composition with a Rational Function
Composition of Logarithmic and Exponential Functions
Composition of Logarithmic and Exponential Functions
Composition of Square Root and Power Functions
Composition of Square Root and Power Functions
Composition of Cube Root and Power Functions
Composition of Cube Root and Power Functions
 
Inverse of Functions
These videos show how to determine if a function has an inverse and then find the inverse.
 
Inverse of a Linear Function
Inverse of a Linear Function
Inverse of a Square Root Function
Inverse of a Square Root Function
Inverse of a Rational Function
Inverse of a Rational Function
Inverse of a Rational Function
Inverse of a Rational Function (2)
Difference Quotient
These videos show how to find the difference quotient and then simplify the answer.
Difference Quotient of a Quadratic
Difference Quotient of a Quadratic
Difference Quotient of a Rational Function
Difference Quotient of a Rational Function
Difference Quotient of a Square Root Function
Difference Quotient of a Square Root Function
Solving Inequalities
These videos show how to make a sign diagram to solve an inequality.
Solving an Inequality with a Polynomial
Solving an Inequality with a Polynomial
Solving an Inequality with a Rational Function
Solving an Inequality with a Rational Function
Solving an Inequality with a Sum of Rational Functions
Solving an Inequality with a Sum of Rational Functions
Solving an Inequality with by Finding a Least Common Denominator
Solving an Inequality with by Finding a Least Common Denominator
Solving an Inequality with a Quadratic Function
Solving an Inequality with a Quadratic Function
Properties of a Quadratic
These videos show how to write a quadratic in standard form and find its absolute maximum or absolute minimum.
Absolute Maximum or Minimum of a Quadratic
Absolute Maximum or Minimum of a Quadratic
Standard Form of a Quadratic
Standard Form of a Quadratic
 
Vectors
These videos explain basic vector properties including vector operations, the dot product, and finding a unit vector.
Component Form and Magnitude of a Vector
Component Form and Magnitude of a Vector
Vector Addition and Subtraction and Scalar Multiplication
Vector Addition and Subtraction and Scalar Multiplication
Dot Product
Dot Product
Finding a Unit Vector
Finding a Unit Vector
Systems of Equations
These videos solve systems of linear equations and one system including a quadratic equation.
Solving a System of Equations
Solving a System of Equations
Solving a System of Equations
Solving a System of Equations (2)
Solving a System of Equations
Solving a System of Equations (3)
Solving a System of Equations
Solving a System of Equations (4)
Solving a System of Nonlinear Equations
Solving a System of Nonlinear Equations
 
Exponential Functions
These videos show how to solve exponential equations, model population size with exponential functions, and find the horizontal asymptote of an exponential function.
Equations with Exponential Functions
These videos solve exponential equations including factoring equations with exponentials.
 
An Equation with an Exponential Function
An Equation with an Exponential Function
An Equation with Exponential Functions of Different Bases
An Equation with Exponential Functions of Different Bases
Factoring a Quadratic-Like Equation with Exponentials
Factoring a Quadratic-Like Equation with Exponentials
Factoring an Equation with Exponentials
Factoring an Equation with Exponentials
 

Applications of Exponential Functions
These videos show how to write an exponential function for the size of a population.
 
Population Model with Exponential Growth
Population Model with Exponential Growth
Population Model with Exponential Decay
Population Model with Exponential Decay
 

Horizontal Asymptotes of Exponential Functions
These videos find the horizontal asymptotes of exponential functions by examining the transformations from a basic exponential function.
 
Horizontal Asymptote of an Exponential Function
Horizontal Asymptote of an Exponential Function
Horizontal Asymptote of an Exponential Function
Horizontal Asymptote of an Exponential Function (2)
Horizontal Asymptote of an Exponential Function
Horizontal Asymptote of an Exponential Function (3)
Logarithmic Functions
These videos show how to use the properties of logarithms, find the domain and vertical asymptote of a logarithmic function, and solve equations with logarithmic functions.
Using Properties of Logarithms
These videos show how to use the properties of logarithms to expand or condense logarithmic expressions.
 
Expanding a Logarithmic Expression
Expanding a Logarithmic Expression
Condensing a Logarithmic Expression
Condensing a Logarithmic Expression
Evaluating Logarithmic Expressions
Evaluating Logarithmic Expressions

Vertical Asymptote of Logarithmic Functions
These videos show how to find the vertical asymptotes of a logarithmic function
 
Vertical Asymptote of a Logarithmic Function
Vertical Asymptote of a Logarithmic Function
Vertical Asymptote of a Logarithmic Function
Vertical Asymptote of a Logarithmic Function (2)
 
Equations with Logarithmic Functions
Solving equations with Logarithmic Functions including finding the \(x\)-intercepts and domain of a logarithmic function.
 
Domain and x intercepts of a Logarithmic Function
Domain and \(x\)-intercepts of a Logarithmic Function
Domain and x intercepts of a Logarithmic Function
Domain and \(x\)-intercepts of a Logarithmic Function (2)
Solving an Equation with Logarithms
Solving an Equation with Logarithms
Solving an Equation with a Logarithmic Function
Solving an Equation with a Logarithmic Function
Trigonometry
These videos are an introduction to trigonometry including how to evaluate trigonometric functions and inverse trigonometric functions, how to solve trigonometric equations, and how to graph trigonometric functions.
Evaluating Trigonometric Functions
These videos show how to evaluate trigonometric functions at an angle given some information about the angle.
 
Evaluating All Six Trigonometric Functions
Evaluating All Six Trigonometric Functions
Evaluating the Other Trigonometric Functions Given Sine
Evaluating the Other Trigonometric Functions Given Sine
Evaluating the Other Trigonometric Functions Given Sine
Evaluating the Other Trigonometric Functions Given Sine (2)
A Composition of Tangent and Arccosine
A Composition of Tangent and Arccosine

Trigonometric Equations
These videos show how to find all solutions of trigonometric equation or find all solutions in a given interval.
 
Solving an Equation with Tangent
Solving an Equation with Tangent
Solving an Equation with Sine and Cosine
Solving an Equation with Sine and Cosine
Factoring a Quadratic-Like Equation with Sine
Factoring a Quadratic-Like Equation with Sine
Solving an Equation with Cosine
Solving an Equation with Cosine
Solving an Equation with Sine
Solving an Equation with Sine


Graphs of Trigonometric Equations
These videos show how to find the properties of a trigonometric function including amplitude, period, phase shift, and vertical shift, and then either graph a trigonometric function or write a trigonometric function for a graph. 
 
Sketching One Period of a Sine Function
Sketching One Period of a Sine Function
ketching One Period of a Cosine Function
Sketching One Period of a Cosine Function
Properties of a Sine Function
Properties of a Sine Function
Find the Cosine Function for a Graph
Find the Cosine Function for a Graph