How many vertical asymptotes does the graph of \(\frac{x-3}{x^2+7x-30}\) have?
I set the denominator equal to 0 and found that x = 3, and x = -10. I thought this meant the answer to the question was 2, but it was wrong. Thanks in advance.
+128474 x - 3
_____________
x^2 + 7x - 30
Notice that the denominator factors as
( x - 3 ) 1
______________ = _____
(x - 3) ( x + 10) x + 10
We will have a vertical asymptote at x + 10 = 0 ⇒ x = -10
And we will have a "hole" at x -3 = 0 ⇒ x = 3
See the graph, here : https://www.desmos.com/calculator/skml1smvwr
[The hole doesn't show....but. trust me...there is one at x = 3 !!! ]
