1. Graphing Absolute Value Functions using Transformations

2. Vocabulary The function f(x) = |x| is an absolute value function.

3. The graph of this piecewise function consists of 2 rays, is v-shaped, and opens up. to the left of x = 0 the line is y = -x to the right of x = 0 the line is y = x Notice that the graph is symmetric across the y-axis because for every point (x,y) on the graph, the point (-x,y) is also on the graph.

4. Vocabulary The highest or lowest point on the graph of an absolute value function is called the vertex. The axis of symmetry of the graph of a function is a vertical line that divides the graph into mirror images.

5. Absolute Value Function Vertex Axis of Symmetry

6. Vocabulary The zeros of a function f(x) are the values of x that make the value of f(x) equal to 0. f(x) = |x| - 3 On this graph, f(x) (or y) is 0 when x = -3 and x = 3.

7. Vocabulary A transformation changes a graph’s size, shape, position, or orientation. A translation is a transformation that shifts a graph horizontally and/or vertically, but does not change its size, shape, or orientation. A reflection is when a graph is flipped over a line. A graph flips vertically when -1. f(x) and it flips horizontally when f(-1x).

8. Vocabulary A dilation changes the size of a graph by stretching or compressing it. This happens when you multiply the function by a number.

9. Transformations y = -a |x – h| + k remember that (h, k) is your vertex reflection across the x-axis vertical stretch a > 1 (makes it narrower) OR vertical compression 0 < a < 1 (makes it wider) horizontal translation (opposite of h) vertical translation

10. Example 1 Identify the transformations. 1. y = 3 |x + 2| - 3 2. y = |x – 1| + 2 3. y = 2 |x + 3| - 1 4. y = -1/3|x – 2| + 1

11. Example 2 Graph y = -2 |x + 3| + 2. What is the vertex? What are the intercepts?

12. You Try: Graph y = -1/2 |x – 1| - 2  compare the graph with the graph of y = |x| What are the transformations?

13. Example 3 Write a function for the graph shown.

14. You Try: Write a function for the graph shown.