Question

Identify the vertical asymptotes of f(x) = 2 over quantity x squared plus 3 x minus 10. Group of answer choices x = 5 and x = 2 x = 5 and x = −2 x = −5 and x = 2 x = −5 and x = −2

Answer 1

The vertical asymptotes of f(x) = 2/ x2 + 3x - 10 is x = -5 and x = 2.

Explanation:

Given, f(x) = 2/(x2 + 3x - 10).

Now, we have to find the factors of x2 + 3x - 10.

By splitting the middle term

x2 + 5x - 2x - 10 = 0

Taking out the common terms

x(x + 5) - 2(x + 5) = 0

So we get,

(x - 2)(x + 5) = 0

x = 2 or -5

Thus, the factors of x2 + 3x - 10 are 2 and -5.

Obviously, neither of these numbers is a factor of the numerator.

Therefore, the vertical asymptotes are the lines whose equations are x = -5 and x = 2.