High School Algebra I Unlocked (2016)
Chapter 9. Manipulating Functions
By the end of this chapter, you will be able to:
•Identify types of transformations
•Perform vertical and horizontal translations
•Determine whether a function is even or odd
•Explain and perform the processes for reflecting, stretching, and compressing functions
Lesson 9.1. Functions: A Review of the Basics
BEFORE BEGINNING THIS CHAPTER, YOU SHOULD BE FAMILIAR WITH:
•solving and graphing linear and quadratic equations
•solving and graphing linear and quadratic functions
•the standard form of quadratic equations and functions
•the vertex form of quadratic equations and functions
Turn back to Lesson 7.1
for a more in-depth review
of function basics.
In Chapter 7, we discussed the basic rules of a function: a relation from a set of inputs to a set of possible outputs, in which the input value affects the output value. Let’s consider the graph of the most basic quadratic function, ƒ(x) = x2:
You’ve graphed lots of quadratic equations by now, and each of them has been a transformation of the function ƒ(x) = x2.
A transformation is simply the result of changing the shape or scale of a point, line, or shape of a function. When discussing transformations, many math textbooks may refer to the original figure as the pre-image, and the transformed image as the image.
In this chapter, we’re going to define and explain how to work with three types of transformations: (1) vertical and horizontal translations, (2) reflections, and (3) vertical and horizontal scaling. Luckily, the rules governing the world of mathematical transformations are straightforward; when you know the rules, you’ll be able to understand, interpret, and graph all sorts of functions with ease. Now let’s get this functions party started.