Question

The function f is given as f(x)=log₂x. Function g is defined as g(x)=f(x-2). What's the asymptote of g(x) ?

Answer 1

The asymptote of g(x) = log₂(x - 2) is x = 2.

Step-by-step explanation:

The function g(x) is defined as g(x) = f(x - 2), where f(x) = log₂x. To find the asymptote of g(x), we need to determine where the function approaches infinity or negative infinity. Since f(x) = log₂x has a vertical asymptote at x = 0 (because log₂x is undefined for x ≤ 0), we can substitute (x - 2) for x in f(x) to find the asymptote of g(x).

g(x) = f(x - 2) = log₂(x - 2)

The asymptote for g(x) is x = 2, as the function approaches negative infinity as x approaches 2 from the left and approaches positive infinity as x approaches 2 from the right.