1. 2.7 Absolute Value Tranformations
College Prep
2.7 Absolute Value Tranformations

2. Warm Up
Using the graphing calculator, graph a scatter plot for the following table which shows oil production y (in thousands of barrels) x years after Write down the equation for the best fitting line and predict the daily oil production in X 1 2 3 4 5 6 7 8 Y
6660
6560
6470
6450
6250
5880
5820
5800
5750

3. Transformation: an adjustment made to the parent function that results in a change in size, shape, position or orientation of the parent function.
shifting (“translating”) the graph up or down,
“translating” the graph left or right
vertical stretching or shrinking
(making the graph more steep or less steep)
Reflecting across x-axis or y-axis

4. Absolute Value Parent Function is: f(x) = |x|
Parent Function: The simplest function in a family
of functions (lines, parabolas, cubic functions, etc.)
Absolute Value Parent Function is: f(x) = |x|
Why does it have this shape?
The highest or lowest point on the graph is called the vertex.

5. Graph the parent function y = |x|
Graph f(x) = |x| + 3
What happened to the graph?
Graph f(x) = |x| - 2
|x| + k is a vertical shift
Shifted up 3
Shifted down 2

6. Graph the parent function y = |x|
Graph f(x) = |x + 3|
What happened to the graph?
Graph f(x) = |x - 2|
|x - h| is a horizontal shift
Shifted left 3
Shifted right 3

7. Without graphing describe the transformation.
f(x) = |x| - 5
f(x) = |x + 7|
f(x) = |x – 4| + 2
f(x) = |x + 5| - 1
Down 5
Left 7
Right 4, up 2
Left 5, down 1

8. Graph the parent function y = |x|
Graph f(x) = -|x|
What happened to the graph?
Graph f(x) = 2|x|
Reflected
across x-axis
Stretched vertically by a factor of 2

9. Graph the parent function y = |x|
Graph f(x) = 0.5|x|
What happened to the graph?
Graph f(x) = -3|x|
Vertical Shrink by a factor of 0.5
a|x| is a vertical stretch or shrink by a factor of a
Stretched vertically by a factor of 3, Reflect across x-axis

10. Without graphing describe the transformation
f(x) = -|x+2| - 7
f(x) = 3|x – 1| + 2
Reflect across x-axis
Left 2
Down 7
Vertical Stretch by a factor of 3
Right 1
Up 2

11. Absolute Value Transformation
Vertical stretch factor
Translates left/right
translating up or down
Reflection across x-axis
a is a stretch if a > 1
a is a shrink if 0 < a < 1

12. Write an Equation for each graph
f(x) = |x – 3|
f(x) = -3|x + 2| + 4

13. Apply the following transformations to the figure above: y = -f(x + 2) + 1 and y = 2f(x)

14. Pg. 127: 3-14 (Describe only – do not draw graph), 15-24, 29-31
Homework
Pg. 127: 3-14 (Describe only – do not draw graph), 15-24, 29-31