Algebra 1 Common Core Student Edition, Grade 8-9

Graphing Absolute

Value Functions

Co m m o n Co r e St a t e St a n d a r d s

F-BF.B.3 Identify the effect on the graph of replacing

f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific

values of k (both positive and negative); find the value of

k given the graphs... Also F-IF.C.7b

MP 1, M P 2, M P 3 , MP 4

Objectives To g ra p h a n a b s o lu te v alu e fu n c tio n

To translate th e graph of an absolute value function

. M A T H E M A T I C A L
'PRACTICES

Lesso n ’

Vocabulary

• a b so lu te v a lu e
  fu n ctio n
  1 p i e c e w i s e
  fu n ctio n
  1 s t e p f u n c t i o n
  1 t r a n s l a t i o n

How can you

compare the graphs?

Look for the

characteristics that

you've studied w ith other

graphs, such as shape,

size, o r in d iv id u a l points.

In th e Solve It you described how one line could b e shifted to result in a second

line. You can use a sim ilar m eth o d to graph absolute value functions. An

absolute value function has a V -shaped graph th a t o pens u p or down. The p aren t

function for th e family of absolute value functions is y = \x \.

A translation is a shift of a graph horizontally, vertically, or both. The result is a graph of

the same size and shape, but in a different position.

Esse n t i a l U n d e r st a n d i n g You can quickly graph absolute value eq u atio n s by

shifting th e graph of y = |x|.

Describing Translat ions

B elow a re th e g ra p h s of y = |x| and y = | x | — 2. H ow a re th e g ra p h s re la te d?

The graphs have th e sam e shape. N otice each p o in t on y = |jc| - 2 is 2 u nits

lower th a n th e corresponding p o in t on y = \x \. The g raph of y = |x| — 2 is the

graph of y = |x| translated dow n 2 units.

3 4 6 Chap t er 5 Linear Funct ions

HE