Question

use transformations of ( f(x)=sqrt{x} ) to graph the following function.
( g(x)=sqrt{x}-4 )
what transformation is needed to graph the function ( g(x)=sqrt{x}-4 )? choose the correct answer below.
a. the graph of ( f(x)=sqrt{x} ) should be shifted 4 units to the right.
b. the graph of ( f(x)=sqrt{x} ) should be shifted 4 units down.
c. the graph of ( f(x)=sqrt{x} ) should be shifted 4 units up.
d. the graph of ( f(x)=sqrt{x} ) should be shifted 4 units to the left.

Explanation:

For a function \(y = f(x)+k\), if \(k>0\), the graph of \(y = f(x)\) is shifted \(k\) units up; if \(k < 0\), the graph of \(y = f(x)\) is shifted \(|k|\) units down.

In the function \(g(x)=\sqrt{x}-4\), we have \(f(x)=\sqrt{x}\) and \(k=- 4\).

Answer:

B. The graph of \(f(x)=\sqrt{x}\) should be shifted 4 units down.