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.
3 videos
Equations of Lines
Writing the different forms for the equations of a line given two points on the line
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3 videos
Factoring
Factoring polynomials
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8 videos
Rational Functions
Performing operations with rational expressions and finding the holes and vertical asymptotes of rational functions
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4 videos
Roots of Functions
Finding the roots of functions
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13 videos
Functions: Domain, Composition and Inverses
Finding the domain and inverse of common functions and finding the composition of two functions
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3 videos
Difference Quotient
Finding the difference quotient and simplifying your answer
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5 videos
Solving Inequalities
Using a sign diagram to solve inequalities
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2 videos
Properties of a Quadratic
Writing a quadratic in standard form and determining its absolute maximum or minimum
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4 videos
Vectors
Calculating vector operations and the dot product and finding a unit vector
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5 videos
Systems of Equations
Solving systems of linear equations and systems including a quadratic equation
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9 videos
Exponential Functions
Solving equations with exponential functions, modeling population size and finding the horizontal asymptote
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9 videos
Logarithmic Functions
Using properties of logarithms, finding the vertical asymptote, and solving equations with logarithmic functions
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13 videos
Trigonometry
Evaluating trigonometric and inverse trigonometric functions, solving trigonometric equations, and graphing trigonometric functions
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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
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Slope-Intercept Form of an Equation for a Line
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Standard Form of an Equation for a Line
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Factoring
These videos show the different methods to factor polynomials.
Factoring a Quadratic
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Factoring a Quadratic (2)
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Factoring by Grouping
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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
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Subtracting Rational Expressions
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Multiplying Rational Expressions
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Dividing Rational Expressions
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Adding Rational Expressions
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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
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Holes and Asymptotes of Rational Functions (2)
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Matching a Rational Function with its Graph
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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
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Roots of a Polynomial
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Roots of a Square Root Function
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Roots of a Function with an Absolute Value
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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
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Domain of a Rational Function (2)
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Domain of Function with Roots
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Domain of a Square Root Function
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Composition of Functions
These videos show how to find the composition of two functions.
Composition of Polynomial Functions
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Function Composition with a Rational Function
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Composition of Logarithmic and Exponential Functions
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Composition of Square Root and Power Functions
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Composition of Cube Root and Power Functions
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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
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Inverse of a Square Root Function
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Inverse of a Rational Function
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Inverse of a Rational Function (2)
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Difference Quotient
These videos show how to find the difference quotient and then simplify the answer.
Difference Quotient of a Quadratic
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Difference Quotient of a Rational Function
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Difference Quotient of a Square Root Function
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Solving Inequalities
These videos show how to make a sign diagram to solve an inequality.
Solving an Inequality with a Polynomial
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Solving an Inequality with a Rational Function
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Solving an Inequality with a Sum of Rational Functions
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Solving an Inequality with by Finding a Least Common Denominator
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Solving an Inequality with a Quadratic Function
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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
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Standard Form of a Quadratic
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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
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Vector Addition and Subtraction and Scalar Multiplication
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Dot Product
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Finding a Unit Vector
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Systems of Equations
These videos solve systems of linear equations and one system including a quadratic equation.
Solving a System of Equations
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Solving a System of Equations (2)
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Solving a System of Equations (3)
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Solving a System of Equations (4)
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Solving a System of Nonlinear Equations
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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
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An Equation with Exponential Functions of Different Bases
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Factoring a Quadratic-Like Equation with Exponentials
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Factoring an Equation with Exponentials
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Applications of Exponential Functions
These videos show how to write an exponential function for the size of a population.
Population Model with Exponential Growth
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Population Model with Exponential Decay
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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
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Horizontal Asymptote of an Exponential Function (2)
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Horizontal Asymptote of an Exponential Function (3)
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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
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Condensing a Logarithmic Expression
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Evaluating Logarithmic Expressions
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Vertical Asymptote of Logarithmic Functions
These videos show how to find the vertical asymptotes of a logarithmic function
Vertical Asymptote of a Logarithmic Function
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Vertical Asymptote of a Logarithmic Function (2)
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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
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Domain and \(x\)-intercepts of a Logarithmic Function (2)
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Solving an Equation with Logarithms
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Solving an Equation with a Logarithmic Function
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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
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Evaluating the Other Trigonometric Functions Given Sine
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Evaluating the Other Trigonometric Functions Given Sine (2)
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A Composition of Tangent and Arccosine
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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
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Solving an Equation with Sine and Cosine
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Factoring a Quadratic-Like Equation with Sine
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Solving an Equation with Cosine
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Solving an Equation with Sine
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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
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Sketching One Period of a Cosine Function
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Properties of a Sine Function
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Find the Cosine Function for a Graph
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