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

A. isn't correct because functions are by their definition different.

B is true. Domain of both is x>0 and range is 1/2 as large. because of 1/2 factor in first function

C is true . because of -2 it is shifted to the right by 2 and it is shrunk vertically by 1/2

D isn't true because ranges are not the same.

Answer 2

We know A is correct because the characteristic function involved is sqrt(x); the multiplying factors simply shrink and enlarge the graph. Therefore, A is true.
The first part of B is true; however, the second part about the ranges being different is incorrect. This is because the values of y, the range, can vary from zero to positive infinity.
The similarity stated in C is true and the (-2) within the square root serves to shift the graph to the right two units. Thus, C is correct.
D is also correct as both functions have the same domain and range, that is 0 to infinity for both domain and range in both cases.