Absolute Value Functions

On a separate piece of graph paper, graph y = -|x + 1|; then click on the graph until the correct one appears.

Upside down house, uneven because the right line is longer.

absolute value

the distance that a number is from zero on the number line; always positive

Choose the equation of the graph shown below:

y = |x + 1| - 3

Which of the following describes how to translate the graph y = |x| to obtain the graph of y = |x| - 4?

4 units down

Which of the following describes how to translate the graph y = |x| to obtain the graph of y = |x + 7|?

7 units left

Which of the following describes how to translate the graph y = |x| to obtain the graph of y = |x - 1| - 1?

1 unit right and 1 unit down

On a separate piece of graph paper, graph y = |x - 3|; then click on the graph until the correct one appears.

It's going down left to right all the way to the line before it shoots up again.

On a separate piece of graph paper, graph y = |x| - 1; then click on the graph until the correct one appears.

Looks like a stick person with it's arms to the sky

On a separate piece of graph paper, graph y = -|x| + 1; then click on the graph until the correct one appears.

Looks like the roof of a house. It's moved up one from the (0,0) line.

translation

a shift or slide of a graph in the coordinate plane

If the graph of y = |x| is translated so that the point (1, 1) is moved to (1, 4), what is the equation of the new graph?

y = |x| + 3