Which of the following statements are true?

Check all that apply.

AThe graph of

f(x)=1/2 √x

looks like the graph of

f(x)=3√x

.

BThe function

f(x)=1/2 3√x

has the same domain as

f(x)=3√x

, but its range is 1/2 as large.

CThe 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.

DThe function

f(x)=1/2 3√x

has the same domain and range as

f(x)=3√x

Aisn'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 Link

scme1702 scme1702 · Answer 2 · 2016-10-07T16:46:28-04:00

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.