2-7 ABSOLUTE VALUE FUNCTIONS

AND GRAPHS

Apply rules for transformations by graphing absolute value functions.

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| + b translates the graph up y = |x| - b 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 . What do you notice? Now try: What do you notice? 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

|| creates a stretch or compressionYou can find the a-value by finding the slope

of the branch to the right. creates a horizontal translation 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

is your a-value Substitute into the general form

Assignment

Odds p.111 #13-33