The document discusses absolute value functions and their transformations. It notes that the graph of an absolute value function looks like a V-shape, and examples absolute value functions modeling bank shots in pool. It then reviews four types of transformations for absolute value functions: vertical reflection, vertical stretch/shrink, horizontal shift, and vertical shift. These transformations can move the vertex and axis of symmetry. Several examples of graphing transformed absolute value functions are provided.

2. The
graph of y = |x| looks like a
v-shape.
vertex
x
-2
-1
0
1
2
y = |x|

3. Have
you ever played pool or
putt-putt golf?
The path of the ball when making
a bank shot is an example of
an absolute
value
function.

4. Remember
our 4 function
transformations?
1. Vertical reflection: y = - |x|
2. Vertical stretch/shrink: y = 2|x|
3. Horizontal Shift: y = |x + 2|
4. Vertical Shift: y = |x| + 2

5. The
vertex will move according to
the horizontal and vertical shifts.
Example:
Vertex: (-3, -4)
x = -3
Axis
of symmetry:
Vertical line
through
the vertex
(-3, -4)

6. Sketch
the parent graph.
Perform transformations.
Example:
Graph
Vertex:
Axis
of symmetry:

7. Graph
Vertex:
Axis
of symmetry:

8. Graph
Vertex:
Axis
of symmetry:

9. Graph
Vertex:
Axis
of symmetry: