Question

f(x) = \sqrt{x}
which statement describes the graph of f(x - 4) relative to the graph of f(x)?
a. the x-intercept of f(x - 4) is 4 less than the x-intercept of f(x).
b. the x-intercept of f(x - 4) is 2 less than the x-intercept of f(x).
c. the x-intercept of f(x - 4) is the same as the x-intercept of f(x).
d. the x-intercept of f(x - 4) is 2 more than the x-intercept of f(x).
e. the x-intercept of f(x - 4) is 4 more than the x-intercept of f(x).

Explanation:

Step1: Find the \(x\)-intercept of \(f(x)=\sqrt{x}\)

Set \(y = f(x)=0\), so \(\sqrt{x}=0\). Solving for \(x\), we get \(x = 0\).

Step2: Find the \(x\)-intercept of \(f(x - 4)=\sqrt{x-4}\)

Set \(y=f(x - 4)=0\), so \(\sqrt{x - 4}=0\). Squaring both sides gives \(x-4=0\), and solving for \(x\) gives \(x = 4\).

Answer:

E. The \(x\)-intercept of \(f(x - 4)\) is \(4\) more than the \(x\)-intercept of \(f(x)\).