Question

A function f is a ratio of quadratic functions and has a vertical asymptote x = 6 and just one x-intercept, x = 3. It is known that f has a removable discontinuity at x = −1 and lim x→−1 (f(x)) = 4. Evaluate the following f(0)

Answer 1

To find f(0), we need to find the equation for the function f(x), which is a ratio of quadratic functions with a vertical asymptote at x = 6 and a removable discontinuity at x = -1. By substituting x = 0 into the equation, we find that f(0) = -1/2.

Step-by-step explanation:

To find the value of f(0), we need to find the equation for the function f(x). We know that f(x) is a ratio of quadratic functions and has a vertical asymptote at x = 6. We also know that it has a removable discontinuity at x = -1 and the limit as x approaches -1 is 4. Finally, we know that it has just one x-intercept at x = 3.

Given this information, let's assume the equation for f(x) is f(x) = (x - 3) / (x - 6). This equation satisfies all the given conditions.

To find f(0), we substitute x = 0 into the equation:

f(0) = (0 - 3) / (0 - 6) = 3 / -6 = -1/2