Functions

What is a Function?

Pre-Quiz

Answer the following questions honestly to assess your own abilities. This pre-quiz will not be graded. It can be used for you to determine your own strengths and weaknesses.

Pre-Quiz Reflection

This optional reflection is intended to be used after completing the previous pre-quiz. It will help you to think about the questions from the pre-quiz, how you did, and what you’re going to do about it.

[Video] Function Notation

We go through common prerequisite topics related function notation, such as evaluation, domain, and range of functions.

[Video] Functions and Their Graphs

We go through common prerequisite topics about functions and their graphs. We look at evaluation, domain, and range with regards to graphs.

Same or different?

Two young mathematicians examine one (or two?) functions.

For each input, exactly one output

We define the concept of a function.

Composition of Functions

[Video] Composition of Functions

In this set of videos, we will work to understand composition of functions, including evaluation of composition of functions through function notation and graphs, building compositions of functions recognition a function composites.

Composition of functions

We discuss compositions of functions.

Review of Common Functions

Polynomials

Pre-Quiz

Answer the following questions honestly to assess your own abilities. This pre-quiz will not be graded. It can be used for you to determine your own strengths and weaknesses.

Pre-Quiz Reflection

This optional reflection is intended to be used after completing the previous pre-quiz. It will help you to think about the questions from the pre-quiz, how you did, and what you’re going to do about it.

Linear functions

On this card, we will review linear functions and a couple of ways of writing linear functions.

[Video] Behavior of Polynomial Graphs

In this set of videos, we will work to understand how polynomials behave and how their graphs look.

How crazy could it be?

Two young mathematicians think about the plots of functions.

Polynomial functions

Polynomials are some of our favorite functions.

Rational Functions

Rational functions

Rational functions are functions defined by fractions of polynomials.

Piece-Wise Functions

[Video] Piece-Wise Functions

In this set of videos, we will work to understand how to find function values of piece-wise functions, how to find the domain and range of piece-wise functions, and how to graph piece-wise functions.

Fractions

Arithmetic and Algebra of Fractions

Pre-Quiz

Answer the following questions honestly to assess your own abilities. This pre-quiz will not be graded. It can be used for you to determine your own strengths and weaknesses.

Pre-Quiz Reflection

This optional reflection is intended to be used after completing the previous pre-quiz. It will help you to think about the questions from the pre-quiz, how you did, and what you’re going to do about it.

Arithmetic of Fractions

On this card, we will review how to add, subtract, multiply, and divide fractions and rational expressions. We will also review what it means to simplify fractions and rational expressions.

Solving Equations and Linear Inequalities

Solving Linear Inequalities

[Video] Solving Linear Inequalities

In this series of videos, we will explore how to find the solutions to algebraic inequalities.

Multiplying and Factoring Polynomials

Pre-Quiz

Answer the following questions honestly to assess your own abilities. This pre-quiz will not be graded. It can be used for you to determine your own strengths and weaknesses.

Pre-Quiz Reflection

This optional reflection is intended to be used after completing the previous pre-quiz. It will help you to think about the questions from the pre-quiz, how you did, and what you’re going to do about it.

Multiplying Polynomials

[Video] Multiplying Polynomials

In this set of videos, we will work to understand how to distribute and multiply polynomials. We will talk about multiplication of two monomials, two binomials, one monomial and one binomial, and polynomials with more terms.

Factoring Polynomials

[Video] Fundamentals of Factoring

We go through common prerequisite topics about fundamentals of factoring. We look at common factors and factoring quadratic polynomials.

Simplifying Rational Functions

Same or different? Take 2

Two young mathematicians examine one (or two?) functions once again.

Simplifying Rational Functions

On this card, we will review how to simplify rational functions with a focus on the domains of the function before and after simplification.

Trigonometry

Trig Functions

Pre-Quiz

Answer the following questions honestly to assess your own abilities. This pre-quiz will not be graded. It can be used for you to determine your own strengths and weaknesses.

Pre-Quiz Reflection

This optional reflection is intended to be used after completing the previous pre-quiz. It will help you to think about the questions from the pre-quiz, how you did, and what you’re going to do about it.

[Video] Triangles to Trig Functions

This series of videos will be aimed at using basic right angle trigonometry and the Pythagorean Theorem to develop an understanding of trigonometric functions and the unit circle and understand how it can be used and how what it means, as well some typical values on the unit circle and of trigonometric functions.

Trigonometric functions

We review trigonometric functions.

Solving Trig Equations

Pre-Quiz

Answer the following questions honestly to assess your own abilities. This pre-quiz will not be graded. It can be used for you to determine your own strengths and weaknesses.

Pre-Quiz Reflection

This optional reflection is intended to be used after completing the previous pre-quiz. It will help you to think about the questions from the pre-quiz, how you did, and what you’re going to do about it.

[Video] Solving Trig Equations

In this series of videos, we will be aimed at learning how solving trigonometric equations.

Geometry of Common 2D and 3D Shapes

2D Shapes

Pre-Quiz

Answer the following questions honestly to assess your own abilities. This pre-quiz will not be graded. It can be used for you to determine your own strengths and weaknesses.

Pre-Quiz Reflection

This optional reflection is intended to be used after completing the previous pre-quiz. It will help you to think about the questions from the pre-quiz, how you did, and what you’re going to do about it.

[Video] Circles: Circumference & Arc Length

In this series of videos, we will talk about geometric measures and will serve as a guide to areas and lengths related to circles.

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