Question

consider the graph of the function (f(x) = 2^x).

which statement describes a key feature of function (g) if (g(x) = f(x - 4))?

horizontal asymptote of (y = -4)

horizontal asymptote of (y = 0)

Explanation:

Identify the transformation

$$ g(x) = f(x - 4) = 2^{x - 4} $$

Determine the horizontal asymptote

$$ \lim_{x \to -\infty} 2^{x - 4} = 0 \implies y = 0 $$

Answer:

• horizontal asymptote of \(y = -4\)
• horizontal asymptote of \(y = 0\) (Correct answer)