Which of the following statements are true? Check all that apply.

Question

Which of the following statements are true? Check all that apply.

A. F(x)=1/2 (3)√(x-2) has the same domain and range as f(x)= 3√x. (the three goes on the hook of the square root symbol on both equations).

B. The graph of f(x)=1/2(3)√x looks like the graph of f(x)= 3√x , but will shrink it vertically by a factor of 1/2. (the three goes on the hook of the square root symbol on both equations).

C. The graph of f(x)=1/2(3)√x looks like the graph of f(x)= 3√x, but will shrink it horizontally by a factor of 1/2. (the three goes on the hook of the square root symbol on both equations).

D. The graph of f(x)=1/2√x looks like the graph of f(x)= 3√x , but will shrink it vertically by a factor of 1/2. (the three goes on the hook of the square root symbol on the second equation).

Answer 1

A False. the domains are different. for sqr(x-2) x must be greater or equal to 2, while for sqr(x), x must be greater or equal to 0.

B True. y=cube root of x is the same as y^3 = x

just cube both sides of the equation. Putting a 1/2 in the equation shrinks the graph vertically.

C False. a vertical shrink would be the same as a horizontal stretch, not a horizontal shrink. You might visualize this better, if you considered y=x and y=x/2

It shrinks the line down, but stretches it to the right with (1/2) as the x coefficient.

D False, unless you intended the 1/2sqrx to be 1/2 times the cube root of x. Maybe a 3 is missing in the first equation. but comparing a square root of x with a cube root of x is not just a vertical shift by a factor of 1/2