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Absolute value functions and transformations.notebook, Exercises of Pre-Calculus

Rice University Pre-Calculus

An absolute value graph has one axis of symmetry that passes through the vertex. Page 3. Absolute value functions and transformations.notebook.

Typology: Exercises

2022/2023

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Absolutevaluefunctionsandtransformations.notebook

October14,2014

Oct123:13PM

AbsoluteValueFunctionsandGraphs

Objective:

Icangraphanabsolutevaluefunction

byperformingtransformationsonthe

parentfunction

(

)=|

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Oct 123:13 PM

Absolute Value Functions and Graphs

Objective:

I can graph an absolute value function

by performing transformations on the

parent function

f

x

Oct 123:15 PM

Vocabulary

· The function f(x) = |x| is an absolute value function.

· The highest or lowest point on the graph of an

absolute value function is called the vertex.

An axis of symmetry of the graph of a function is a

vertical line that divides the graph into mirror images.

An absolute value graph has one axis of symmetry

that passes through the vertex.

Oct 123:21 PM

Building the Absolute Value Function

The absolute value function is

defined by f (

x ) = |

x |.

Oct 123:30 PM

This is the absolute value parent function.

Table

x

y

f(x)=lxl

Oct 123:35 PM

Translation

A translation is a

transformation

that shifts a graph

horizontally or

vertically, but

doesn’t change

the overall shape

or orientation.

Oct 1410:28 AM

Oct 1410:41 AM

Oct 1410:30 AM

Oct 1411:08 AM

Oct 1411:10 AM

Oct 123:41 PM

y = a |x – h| + k

Oct 123:50 PM

Multiple Transformations

In general, the graph of an absolute value function

of the form

y

a

x

h

k

can involve

translations, reflections, stretches or compressions.

To graph an absolute value function, start by

identifying the vertex

Oct 123:52 PM

Example 1

Graph the following function without making a table.

y = | x – 2| + 3

Vertex

How does this graph move?

Did this graph stretch or compress?

(slope of 1)

Oct 123:56 PM