Question

What is the equation of the vertical asymptote for f(x) = log(x - 2)?

a) x = ²
b) y = ²
c) y = -²
d) x = ⁰

Answer 1

The vertical asymptote of the function f(x) = log(x - 2) is x = 2, since the logarithm becomes undefined at that point.

Step-by-step explanation:

The equation of the vertical asymptote for the function f(x) = log(x - 2) can be determined by looking at the properties of logarithms. A logarithmic function approaches a vertical asymptote when its argument approaches zero since the logarithm of zero is undefined. In this case, the argument of the logarithm is (x - 2).

Therefore, the vertical asymptote occurs where x - 2 = 0, which solves to x = 2. Hence, the correct equation for the vertical asymptote is x = 2.

The equation of the vertical asymptote for the function f(x) = log(x - 2) is x = 2.