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
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3 videos
Equations of Lines
Writing the different forms for the equations of a line given two points on the line

3 videos
Factoring
Factoring polynomials

8 videos
Rational Functions
Performing operations with rational expressions and finding the holes and vertical asymptotes of rational functions

4 videos
Roots of Functions
Finding the roots of functions

13 videos
Functions: Domain, Composition and Inverses
Finding the domain and inverse of common functions and finding the composition of two functions

3 videos
Difference Quotient
Finding the difference quotient and simplifying your answer

5 videos
Solving Inequalities
Using a sign diagram to solve inequalities

2 videos
Properties of a Quadratic
Writing a quadratic in standard form and determining its absolute maximum or minimum

4 videos
Vectors
Calculating vector operations and the dot product and finding a unit vector

5 videos
Systems of Equations
Solving systems of linear equations and systems including a quadratic equation

9 videos
Exponential Functions
Solving equations with exponential functions, modeling population size and finding the horizontal asymptote

9 videos
Logarithmic Functions
Using properties of logarithms, finding the vertical asymptote, and solving equations with logarithmic functions

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

SlopeIntercept 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 (2)

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

Subtracting Rational Expressions

Multiplying Rational Expressions

Dividing 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 (2)

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 Polynomial

Roots of a Square Root Function

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 (2)

Domain of Function with Roots

Domain of a Square Root Function

Composition of Functions
These videos show how to find the composition of two functions.
Composition of Polynomial Functions

Function Composition with a Rational Function

Composition of Logarithmic and Exponential Functions

Composition of Square 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 Square Root 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 Rational 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 Rational Function

Solving an Inequality with a Sum of Rational Functions

Solving an Inequality with by Finding a Least Common Denominator

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

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

Vector Addition and Subtraction and Scalar Multiplication

Dot Product

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 (2)

Solving a System of Equations (3)

Solving a System of Equations (4)

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 Exponential Functions of Different Bases

Factoring a QuadraticLike 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 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 (2)

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

Condensing a Logarithmic Expression

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 (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 (2)

Solving an Equation with Logarithms

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 the Other Trigonometric Functions Given Sine

Evaluating the Other Trigonometric Functions Given Sine (2)

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 Sine and Cosine

Factoring a QuadraticLike Equation with Sine

Solving an Equation with Cosine

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 Cosine Function

Properties of a Sine Function

Find the Cosine Function for a Graph
