1. Warm-Up
1. On approximately what interval is the function is decreasing. Are there any zeros? If so where?
Write the equation of the line through the points (-3, 17) and (-15, 29).

2. Lesson 2.1: Graphing Absolute Value Functions
We will be working on the following:
Translating f(x) = |x| up, down, left and right
Stretching and compressing f(x) = |x| vertically and horizontally
Reflecting f(x) = |x| over the x-axis and y-axis
Combinations of the above

3. Vertical and Horizontal Translations
Given the parent function f(x) = |x|, f(x) = |x| + k is a vertical translation. If k is positive, translate up k units. If k is negative, translate down k units. f(x) = |x - h| is a horizontal translation. If h is positive, translate right h units. If h is negative, translate left h units.

4. Example
For each of the following, describe how the parent function f(x) = |x| is transformed.
f(x) = |x| - 6
This is a translation down 6 units.
f(x) = |x+5|
This is a translation left 5 units.

5. Vertical Stretch or Compression
Given the parent function f(x) = |x|, f(x) = a|x| is a vertical stretch or compression by a factor of a. If a > 1, then vertical stretch. If 0 < a < 1, then vertical compression

6. Horizontal Stretch or Compression
Given the parent function f(x) = |x|, f(x) = |bx| is a horizontal stretch or compression by a factor of . If b > 1, then horizontal compression. If 0 < b < 1, then horizontal stretch.

7. Example
For each of the following, describe how the parent function f(x) = |x| is transformed.
f(x) = 5|x|
This is a vertical stretch by a factor of 5.
f(x) = | x|
This is a horizontal stretch by a factor of 2.

8. Reflection over x-axis or y-axis
Given the parent function f(x) = |x|, f(x) = -|x| is a reflection over x-axis. f(x) = |-x| is a reflection over y-axis.

9. Example
For each of the following, describe how the parent function f(x) = |x| is transformed.
f(x) = -|x| + 3
This is a reflection over x-axis and then translated up 3 units.
f(x) = 5|x+3| - 7
This is a vertical stretch by a factor of 5 and then a translation 3 units to the left and 7 units down.