Algebra 1 Common Core Student Edition, Grade 8-9

^ Got It? 1. a. How is th e graph at th e right related to th e graph of

y = |x|?

b. Reasoning W hat are th e do m ain an d range of each

function in Problem 1?

J

I h e g raph of y = \ x \ + k is a tran slatio n of y = | x \. Let k be a positive num ber. Then

y= \x\+ k translates th e graph of y = |x| u p A; units, w hile y = |x| - k translates the

graph of y = |x| down k u n i t s.

Pr o b l em 2 Gr ap h i n g a Ver t i cal Tr an sl at i o n

W h at is th e g ra p h o f y = |x| + 2?

• The equation of an H W
  absolute value function


• The graph of y = |x|

JJeed

The graph o f the

function

Plan

Identify the direction and am ount of

th e tra n s la tio n. Translate th e y -in te rc e p t

point and one point on each side of it.

Draw the graph.

Thm k^^
Why start with the
graph of y = |x|?
Since y = |x | is th e
p a re n t fu n c tio n o f
y= |x| + 2 , y o u c a n
start w ith the graph of
y = |x | and s h ift it up.

Draw the graph of

y = | x | + 2 by

translating the graph

ofy = | x | up 2 units.

Start w ith

the graph of

For a positive n u m b e r h, y = \x + h\ translates th e g raph of y = |x| left h units, an d

y = |x — h\ translates th e g raph of y = |x| right h u n its.

Go t I t? 2. W hat is th e g raph of y = |x| — 7?

The graphs below show w h at h a p p e n s w h e n you graph y = | x + 2 1 a n d y = | x — 2 1.

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PowerAlgebra.com [ Lesson 5-8 Graphing Absolute Value Functions^347