Question

What are the vertical asymptote(s) of y= (x-6)/(x+8) (x-7)

Answer 1

x = -8 and x = 7.

Explanation:

The vertical asymptotes are lines that the function will never touch.

Since no number can be divided by 0, the function will not touch points where the denominator of the function is equal to 0.

`(x - 6)/((x + 8)(x - 7))`, so the vertical asymptotes will be where (x + 8) = 0 and (x - 7) = 0.

x + 8 = 0

x = -8

x - 7 = 0

x = 7

The vertical asymptotes are at x = -8 and x = 7.

Hope this helps!

Answer 2

x = -8 and x= 7

Explanation:

recall that for a rational expression, the vertical asymptotes occur at x-values that causes the expression to become undefined. These occur when the denominator becomes zero.

Hence the asymptototes will occur in x-locations where the denominator , i.e

(x+8)(x-7) = 0

solving this, we get

(x+8) = 0 ----> x = -8

or

(x-7) = 0 ------> x = 7

hence the asymptotes occur x = -8 and x= 7