Question

what is the effect on the x - intercept of the graph of ( f(x)=sqrt3{x} ) when ( f(x) ) is replaced by ( f(x + 5) )? (1 point)
the x - intercept shifts to the right by a distance of 5.
the x - intercept shifts up by a distance of 5.
the x - intercept shifts down by a distance of 5.
the x - intercept shifts to the left by a distance of 5.

Explanation:

Step1: Find the x - intercept of \(y = f(x)=\sqrt[3]{x}\)

Set \(y = 0\), then \(0=\sqrt[3]{x}\), so \(x = 0\).

Step2: Find the x - intercept of \(y=f(x + 5)=\sqrt[3]{x+5}\)

Set \(y = 0\), then \(0=\sqrt[3]{x + 5}\). Cubing both sides gives \(0=x + 5\), so \(x=-5\).

Answer:

The \(x\) - intercept shifts to the left by a distance of \(5\).