Question

Describe the vertical asymptote(s) and hole(s) for the graph of y = (x-5)(x-2) over (x-2)(x+4).

Answer 1

X=-3 ,-1

Explanation:

Answer 2

To find where there are holes, we need to make the function =
`(0)/(0)`.

`((x-5)(x-2))/((x-2)(x+4))`
If you plug in
`x=2`, you get
`(0)/(0)`, which means there is a hole in the graph when
`x=2`

To find where there are vertical asymptotes, we need to make just the bottom 0.
Ex.
`(1)/(0)`

`((x-5)(x-2))/((x-2)(x+4))`
If you plug in
`x=-4`, you get
`((-9)(-6))/(0) = (54)/(0)`, which means there is a vertical asymptote when
`x=-4`