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

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.

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.