# 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 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 Slope-Intercept 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.
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
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 Quadratic-Like 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 Quadratic-Like 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