Question

determine the y-intercept(s) of the following function. enter your answers as points in the form (a, b). separate multiple y-intercepts with a comma. if there is no y-intercept, enter none. f(x) = (x - 6)/(x² - 8)

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a function \(y = f(x)\) is the point where \(x = 0\) (since it lies on the y - axis, where the x - coordinate is 0). So we need to find \(f(0)\) for the function \(f(x)=\frac{x - 6}{x^{2}-8}\).

Step2: Substitute \(x = 0\) into the function

Substitute \(x = 0\) into \(f(x)=\frac{x - 6}{x^{2}-8}\). We get \(f(0)=\frac{0 - 6}{0^{2}-8}=\frac{-6}{-8}=\frac{3}{4}\).

Answer:

\((0,\frac{3}{4})\)