Download Parent Functions and Transformations Objectives • Identify, graph

Pre – Calculus
Unit 1
Section 1.5 Notes: Parent Functions and Transformations
Objectives
• Identify, graph, and describe parent functions.
• Identify and graph transformations of parent functions
Family of Functions
 A group of functions with graphs that display similar characteristics
 Parent function: simplest of the functions in a family
Family: 𝑓(𝑥) = 2√𝑥 − 3
𝑓(𝑥) = √𝑥 + 3 − 4
𝑓(𝑥) = −√𝑥 − 5
Parent: 𝑓(𝑥) = √𝑥
Step Function
 A piece-wise function in which the graph resembles a set of stairs
 Most well known step function is greatest integer function:
Example 1: Describe the following characteristics of the graph of the parent function: domain, range, intercepts, symmetry,
continuity, end behavior, and intervals on which the graph is increasing/decreasing.
a) f(x) =
1
𝑥
b) f(x) = x 2
Transformations
 A change in the location, size, or shape of a graph
 Rigid transformations: change only position
 Nonrigid: distort graph shape
 Translation: rigid transformation that shifts the graph (up or down, left or right)
Example 2: Use the graph of f (x) = x3 to graph the given function.
a) g (x) = x3 – 2.
b) g (x) = (x – 1)3.
c) g (x) = (x – 1)3 – 2
Reflection: rigid transformation that produced a mirror image with respect to a line
Example 3: Describe how the graphs of f(x) = √𝑥 and g(x) are related. Then write an equation for g(x).
a)
b)
Dilation: nonrigid transformation that compresses or expands a graph
Example 4:
3
a) Identify the parent function f (x) of g(x) = , and describe how the graphs of g (x) and f (x) are related. Then graph f (x) and g (x) on
𝑥
the same axes.
b) Identify the parent function f (x) of g (x) = –|4x|, and describe how the graphs of g (x) and f (x) are related. Then graph f (x) and g (x)
on the same axes.
Example 5:
a) Graph
b) Graph
Example 7:
a) Use the graph of f (x) = x 2 – 4x + 3 to graph the function g(x) = |f (x)|.
b) Use the graph of f (x) = x 2 – 4x + 3 to graph the function h (x) = f (|x|).