# Functions

Mathematics III,

A great cook knows how to take basic ingredients and prepare a delicious meal. In this topic, you will become function-chefs! You will learn how to combine functions with arithmetic operations and how to compose functions. You will also learn how to transform functions in ways that shift, reflect, or stretch their graphs. Finally, you will learn about inverse functions and how to find them!

This course contains 9 segments:

Combining functions

Learn how to take two basic functions and combine them into a new function which is their sum, difference, product, or quotient.

Composing functions

Learn what function composition is, how to to work with composite functions, and how to find the formulas of the composition of two functions.

Modeling situations by combining & composing functions

Make use of knowledge in combining and composing functions, by modeling complex real-world situations.

Shifting functions

Learn how to transform functions so their graph is shifted horizontally or vertically. Learn how to find the equation of a function that is a shift of another function.

Stretching functions

Learn how to transform functions so their graph is stretched horizontally or vertically. Learn how to find the equation of a function that is a stretch of another function.

Introduction to inverses of functions

Learn what inverses of functions are, and gain some experience with them by finding the outputs of the inverse of a function given that function.

Finding inverse functions

Learn how to find the inverses of polynomials functions, radical functions, and rational functions.

Verifying that functions are inverses

Learn how to check whether a pair of functions are the inverses of one another.

Determining whether a function is invertible

Learn about the conditions for a function to be invertible, and learn how to manipulate functions to make them invertible.

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