2-7 Absolute Value Functions and Graphs Apply rules for transformations by graphing absolute value functions. 2-7 Absolute Value Functions and Graphs

Absolute Value Function V-shaped graph that opens up or down Up when positive, down when negative Parent function: y = |x| Axis of symmetry is the vertical axis through the middle of the graph. Has a single maximum point OR minimum point called the vertex.

Translation Shift of a graph horizontally, vertically, or both. Same size and shape, different position

Try it. Create a table and sketch the graph of the following: y = |x| + 2 y = |x| - 3 What do you notice?

Vertical Translation Start with the graph of y = |x| y = |x| + k translates the graph up y = |x| - k translates the graph down

Try this. Create a table and sketch the graph of the following: y = |x + 3| y = |x – 1| What do you notice?

Horizontal Translation Start with the graph of y = |x| y = |x + h| translates the graph to the left y = |x – h| translates the graph to the right.

Vertical Stretch and Compression Use a table to graph 𝑦=3|𝑥|. What do you notice? Now try: 𝑦= 1 3 |𝑥| When the coefficient is greater than 1 we have a vertical stretch (making the graph narrower) Between 0 and 1 we have a compression (making the graph wider)

General Form 𝑦=𝑎 𝑥−ℎ +𝑘 |𝑎| creates a stretch or compression You can find the a-value by finding the slope of the branch to the right. ℎ creates a horizontal translation 𝑘 creates a vertical translation The vertex is located at (h,k) The axis of symmetry is the line x = h

Writing Absolute Value Functions What is the equation of the absolute value function? Vertex: (-1,4) So h = -1 and k = 4 Find the slope of the branch to the right − 1 3 is your a-value Substitute into the general form 𝑦=− 1 3 𝑥+1 +4

Assignment Odds p.111 #13-33