Module 10: Linear and Quadratic Function Families

The graph of the linear parent function y = x (left). The graph of the quadratic parent function y = x2 (right).

A function family includes a parent function and all transformations of the parent function. In this module, you will analyze the linear and quadratic function families, and explore their characteristics algebraically and graphically. You will learn how to determine the domain and range of a function, and in turn, find function values for elements of the domain. You will also learn how to find the zeros and intercepts of linear and quadratic functions.

Getting Started

As explained in the Introduction, a function family includes a parent function and all transformations of the parent function. Consider the graphs of the linear and quadratic parent functions given above. What similarities do you notice between the graphs? What differences do you notice? Can you think of ways that the graphs of the parent functions can be transformed to create new members of each function family?

Analyze the graphs of the parent functions and list the similarities and differences that you notice. Also, list the transformations that could be applied to each parent function.

Key Vocabulary

To view the definitions for these key vocabulary terms, visit the course glossary.