Question

It this a function and explain why?

Answer 1

\[y=\frac{6}{\left|x\right|}\]

Answer 2

it passes the vertical line test.
so it's a function. however, it is not defined at x=0

Answer 3

https://www.desmos.com/calculator looking at this don't the lines touch eventually? @phi

Answer 4

*doesn't

Answer 5

as you get close to x=0 (from either side), the lines get closer together.
but they never do touch. We deal with that by saying the function is not defined at x=0
i.e. its domain is (-infinity , +infinity) but x \( \ne\) 0

Answer 6

Thanks Phi!! I appreciate you time and help!