Absolute Value Reasoning

Question

Which if any, of the relations described by the equations y= the absolute value of x, x= the absolute value of y, and the absolute value of x= the absolute value of y represent functions? Explain

Answer 1

The definition of a function is that every x value may have one and only one corresponding y value.

 

Graphically we can test this by something called the VLT or vertical line test. If an equation is a function you must be able to draw a vertical line through it at any x value within it's range and it may only intersect with the function once.

 

 

You can test this by choosing arbitrary x values and find the corresponding y:

 

y = |x| will give a line at a 45° angle in the positive x and y directions, this passes a VLT so it is a function

 

|y| = x will give 2 lines one heading at a 45° angle in the positive x and y direction and one heading at a -45° angle in the positive x and negative y direction. This will fail the VLT so it is not a function.

 

|y| = |x| will give two lines intersecting at the origin, perpendicular to each other. This will also fail the VLT and is not a function.