Question

Which of the following statements are true?

Check all that apply.

A. The graph of
f(x)=1/2 √x
looks like the graph of
f(x)=3√x
.
B. The function
f(x)=1/2 3√x
has the same domain as
f(x)=3√x
, but its range is 1/2 as large.
C. The graph of
f(x)=1/2 3√(x-2)
looks like the graph of
f(x)=3√x
, except it is shifted right and shrunk vertically by a factor of 1/2.
D. The function
f(x)=1/2 3√x
has the same domain and range as
f(x)=3√x

Answer 1

The correct statements are B and C.

Step-by-step explanation:

To determine which of the statements are true, let's consider each one:

A. The graph of f(x) = 1/2 √x does not look like the graph of f(x) = 3√x. The first graph is a horizontal line while the second graph is a curve.

B. The function f(x) = 1/2 3√x has the same domain as f(x) = 3√x, but its range is not 1/2 as large. The range of f(x) = 1/2 3√x is actually half the range of f(x) = 3√x.

C. The graph of f(x) = 1/2 3√(x-2) does look like the graph of f(x) = 3√x, but it is shifted to the right by 2 units and vertically shrunk by a factor of 1/2.

D. The function f(x) = 1/2 3√x does not have the same domain and range as f(x) = 3√x. The domain remains the same, but the range is halved.

Based on this analysis, the correct statements are B and C.