Graphs Involving Absolute Value

Question 1

What is Absolute Value?

Answer 1

The taking of any number and making it become (or stay) positive.

Question 2

What is the Translation Rule for an Absolute Value Function?

Answer 2

In the graph of y=x+c, the translated form will be y=x shifted c units up/down. (If in the equation x+c/x-c are grouped together in absolute value symbols, it will be y=x shifted to c units left or right)

Question 3

What is the Reflection Rule for Absolute Value Functions?

Answer 3

The graph of y=-x is the graph of y=x reflected across the x-axis.

Question 4

What is the Scaling Rule for Absolute Value Functions?

Answer 4

When c>1, the graph of y=cx is the graph of y=x stretched vertically by a factor of c. When c<1, the graph of y=cx is the graph of y=x compressed vertically by a factor of c.