Combinations of Functions

Quick Review

What you’ll learn about Combining Functions Algebraically Composition of Functions Relations and Implicitly Defined Functions … and why Most of the functions that you will encounter in calculus and in real life can be created by combining or modifying other functions.

The Identity Function

The Squaring Function

The Cubing Function

The Reciprocal Function

The Square Root Function

The Exponential Function

The Natural Logarithm Function

The Sine Function

The Cosine Function

The Absolute Value Function

The Greatest Integer Function

The Logistic Function

Example Looking for Domains One of the functions has domain the set of all reals except 0. Which function is it?

Example Looking for Domains One of the functions has domain the set of all reals except 0. Which function is it?

Example Analyzing a Function Graphically

Sum, Difference, Product, and Quotient

Example Defining New Functions Algebraically

Composition of Functions

Example Composing Functions

Example Decomposing Functions

Example Using Implicitly Defined Functions