Question

Which statement accurately describes whether the function f(x) = 8(x-1)² has a vertical asymptote at x = 8?

A. There is a vertical asymptote at x = 8 because limₓ→8 f(x) = 8.
B. There is not a vertical asymptote at x = 8 because limₓ→8 f(x) does not exist.
C. There is a vertical asymptote at x = 8 because limₓ→8 f(x) = 0 and limₓ→8⁺ f(x) = 0.
D. There is not a vertical asymptote at x = 8 because limₓ→8 f(x) and limₓ→8⁺ f(x) are not opposites.

Answer 1

The function f(x) = 8(x-1)² does not have a vertical asymptote at x = 8 because the limit of the function as x approaches 8 does not exist.

Step-by-step explanation:

The correct statement that accurately describes whether the function f(x) = 8(x-1)² has a vertical asymptote at x = 8 is B. There is not a vertical asymptote at x = 8 because limₓ→8 f(x) does not exist.

To determine if a function has a vertical asymptote at a certain value of x, we need to check if the limit of the function as x approaches that value exists. In this case, we need to find the limit of f(x) as x approaches 8. We can do this by plugging in the value of 8 into the function and simplify: f(x) = 8(8-1)² = 8(7)² = 8(49) = 392. Therefore, the limit of f(x) as x approaches 8 is 392, which means there is not a vertical asymptote at x = 8.