Absolute Value

```Absolute Value
Definition
,
0,   = 0
lxl =
−,
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
3.5
3
2.5
2
y
y = lxl
1.5
1
0.5
0
-4
-2
0
x
2
4
Vertex – highest of lowest point on the graph
of an absolute value function. For this graph
the vertex is (0,0).
Transformations
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 = lx-hl + k
Y=lxl
(h,k)
k
(0,0)
h
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.
The graph is narrower.
For lal<1
The graph is vertically
shrunk, or compressed.
The graph is wider.
Choose one and graph it with your table!
a = 3, 5, ½ , or ¼
Reflections (FLIPS)
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.
Example
y = -3 lx-1l +2
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