Question

Question #16cae

Answer 1

Have you tried graphing the function?

Here it is:
graph{y=2/x [-10, 10, -5, 5]}

Looking at the ends of the x-axis and examining the function horizontally, it becomes clear that the

Domain:

All real numbers except 0

Looking at the ends of the x-axis and examining the function horizontally, it becomes clear that the

Range:

All real numbers except 0

Explanation:

BUT WHY?

Domain:

(if x=0, then the function is undefined)

Range:

Although the function approaches zero, there is no possible value for x that would make y=0, so the function never touches the x-axis or y=0

This is quite simple to understand although it may take some time.
I recommend you to try and find the asymptotes of graphs like these, which are lines that the function never touches or crosses.

Hope that helps!