Question

When the function y=x is changed to y=|x|, how is the graph affected?

A. All points for x 0 are reflected over the line y=x.
B. All points for x 0 are reflected over the line y=x.
D. All points for x > 0 are reflected over the x-axis.

Answer 1

First, the function:

y = x

Is:

Positive if x > 0

Negative if x < 0

Now, on another hand, the function y = IxI is:

Positive if x < 0

Positive if x > 0.

Then the only part that changes is the negative side of the domain, and the thing that changes is the sign (the change of sign is equivalent to a reflection over the x-axis or the line y = 0".

Then the correct option is:

"All points for x < 0 are reflected over the x-axis"

I suppose that this is option C, the missing one.