Do Now Make a table for –2 ≤ x ≤ 2 and draw the graph of: y = 2 x (Problem #1 from today’s packet)

Absolute Value Functions Absolute value functions are functions that contain absolute value in their equations. The most basic absolute value function is: y = |x|

First We’ll Graph a Similar Equation… The line y = x

Let’s Compare Tables xy xy = |x|y y = xy = |x|

Let’s See What Happens On The Graph

Adding a Coefficient Inside xy xy = |2x|y y = |x|y = |2x|

The graph gets steeper on both sides and closer to its line of symmetry.

In Your Calculator Let’s look at: y = |4x| y = | x |

y = |– 2x| xy xy = |– 2x|y y = |2x|y = |– 2x|

The graph of the absolute value function takes the shape of a V.

What are some observations that you can make about these graphs?

1. As the coefficient of x gets larger, the graph becomes steeper, closer to its line of symmetry. 2. As the coefficient of x gets smaller, the graph becomes less steep, further from its line of symmetry. 3. If the coefficient of x is negative, the graph is the same as if that coefficient were positive. Absolute value changes negative values to positive values.

Notice that the graphs of these absolute value functions are on or above the x-axis. Absolute value always yields answers which are positive or zero.

In Your Calculator Let’s look at: y = |x| + 3 y = |x| – 5

Challenge See if you can shift the graph right or left by adding or subtracting a number from somewhere else in the equation. y = |x + 3| y = |x – 5|

Summary Adding or subtracting a number outside the absolute value shifts the graph up or down. Adding or subtracting a number inside the absolute value shifts the graph right or left.