Question

Identify the vertical asymptotes of f(x) = 10 over quantity x squared minus 7x minus 30.

a) x = 10 and x = 3
b) x = 10 and x = −3
c) x = −10 and x = 3
d) x = −10 and x = −3

Answer 1

The vertical asymptotes of the function f(x) = 10/(x^2 - 7x - 30) are found by setting the factors of the denominator to zero, which gives x = 10 and x = -3 as the points where the function is undefined. These correspond to choice (b).

Step-by-step explanation:

To identify the vertical asymptotes of the function f(x) = \frac{10}{x^2 - 7x - 30}, we must determine the values of x for which the denominator is zero, as these are the points at which the function will be undefined, and vertical asymptotes potentially occur.

The denominator can be factored as follows:

x^2 - 7x - 30 = (x - 10)(x + 3)

Setting each factor equal to zero gives us the potential asymptotes:

• x - 10 = 0 → x = 10
• x + 3 = 0 → x = -3

Therefore, the vertical asymptotes are x = 10 and x = -3, which corresponds to choice (b).