𝑥, 𝑖𝑓 𝑥 𝑖𝑠 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 lxl = 0, 𝑖𝑓 𝑥 = 0
−𝑥, 𝑖𝑓 𝑥 𝑖𝑠 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒
If x = 3, then the absolute value of x = 3.
If x = -3, then the absolute value of x = -(-3), or x = 3.

Parent Function Graph y = lxl
2
1,5
1
0,5
3,5
3
2,5
0
-4 -2 0 2 4 x
Vertex – highest of lowest point on the graph of an absolute value function. For this graph the vertex is (0,0).

A transformation changes a graph’s size , shape , position , or orientation .
A translation is a transformation that shifts a graph horizontally and/or vertically. It does NOT change its size, shape, or orientation – only the position .

Translation of Absolute Value Graph
The graph of y = lx-hl + k is the graph of y = lxl translated h units horizontally and k units vertically. The vertex of is (h,k).
Y=lxl
(0,0) h
(h,k) k y = lx-hl + k

Graph y = lx+5l – 1. Compare with the graph of y = lxl.
Step 1 : Identify and plot the vertex.
Step 2 : Plot another point on the graph. Use symmetry to plot a third point.
Step 3 : Connect the points with a V-shaped graph.
Step 4 : Compare the graphs. Use the word translated in your comparison. How did domain and range change?

Stretches and Shrinks
The graph y = alxl is a vertical stretch or shrink of the graph y = lxl when a ≠ 1.
For lal > 1
The graph is vertically stretched, or elongated.
For lal<1
The graph is vertically shrunk, or compressed.
The graph is narrower.
The graph is wider.
Choose one and graph it with your table!
a = 3, 5, ½ , or ¼

When a = -1, then y = alxl is a reflection in the x-axis of y = lxl. When a is negative number besides -1, it is a vertical stretch or shrink with a reflection across the x-axis.
Y = lxl
Y = -lxl

Multiple Transformations
A graph may be related to a parent graph by even more than 2 transformations. y = a lx-hl +k can involve a stretch or shrink, a reflection, and a translation of y = lxl.

y = -3 lx-1l +2 Stop and think about what each part does.
y = a lx-hl +k h,k translates the graph. The new vertex would be (1,2).
lal tells you whether you shrink or stretch. Since 3 > 1 then the graph is narrower – vertically stretched.
Negative a means you flip so since here we have -3 the graph will be flipped.

Put it into practice
Do the following problems with your shoulder partner.
Pg. 127: 3-7