Absolute Value Functions!!
Day One
Should we do this later?
No, DO NOW
Complete the Absolute Value Exploration Sheet
with a Pal

Hot News!
 After School Help w/Mr. Meyer in the Media Center
 Every Wednesday 2:15-3:00 PM
 Tuesdays and Thursdays by Appointment (Send me
an email or ask me the day before)
 tmeyer2@eden.rutgers.edu
 http://honorsalgebra2meyer.wikispaces.com/
That’s an Aardvark!
f(x)=|x|
Reflect Part of y=x
f(x)=a*|x|
f(x)=|x-h|
f(x)=|x|+k
Rules for Graphing Absolute Value
Functions
 The graph of f(x)=a*|x-h|+k has the following
characteristics:
 A) Vertex (h,k), symmetric with x=h
 B) V-shaped, opens UP if a>0 and DOWN if a<0

C) Wider than parent function if |a|<1 and
narrower than parent function if |a|>1
Graph These Absolute Value
Functions
Graphing!
1) Find the vertex.
(1,1)
2) “a” is negative, and so, it opens downwards.
3) Find one other point on the graph. (Use the slope.)
(2,0)
4) Use symmetry to plot the point on the other side of
the vertex.
Writing Equations
 1) Identify the vertex.
(3,1)
 2) Identify the a value.
Point (4,3) is on the graph.
3=a*|4-3|+1.
a=2
 3) Substitute into y=a*|x-h|+k.
y=2*|x-3|+1
Write it Piecewise!
Write the absolute value equation
as a piecewise function.
1) So if x £ 3 , the equation of
the line is found as follows:
a-Slope is -2 from the graph
c-The point (2,3) is on the line. Use
this to find the intercept:
f(x)=-2x+b
3=-2*(2)+b, b=7.
So if x £ 3, the line has equation
f(x)=-2x+7
Write it Piecewise
2) So if x>3, the equation of the line
is found in the same way to be
f(x)=2x-5.
3) Write it together as a piecewise
as:
{
f(x)= -2x+7; (-∞, 3]
2x-5; (3, ∞)
Practice
 Hit “Y=“
 Enter into Y1 a function of the form f(x)=a*|x-h|+k
 To get absolute value, hit ‘MATH’, scroll right to
‘NUM’, and hit 1:abs(
 For this exercise, pick a, h, and k (your parameters)
between -5 and 5.
 Hit ‘GRAPH’
 Trade calculators with your partner and try to come
up with the absolute value and piecewise equations
for your partners graph.
Graphing Calculators
 On your graphing calculators, graph f(x)= .
(Hit “Y=“, Enter “
“ after Y1, Be Sure to Close the
Parentheses, Hit “GRAPH”) What do you see?