Can anyone check my answer?

Question

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

 

F(x)=1/2cube root-2 has the same domain and range as f(x)=cube root .

The graph of f(x)=1/2cube root looks like the graph of f(x)=cube root , but will shrink it vertically by a factor of 1/2.

The graph of f(x)=1/2cube root looks like the graph of f(x)=cube root , but will shrink it horizontally by a factor of 1/2.

The graph of f(x)=1/2√x looks like the graph of f(x)= cube root, but will shrink it vertically by a factor of 1/2.

All of the answers choices look false to me. The second pair choice looks similar but I'm not sure if its correct.

Answer 1

1. As far as the domain and range are concerned, multiplying a function by a constant won't affect the domain or the rage of the function, unless the function is restricted over a certain interval, which it isn't in this case. 
2. Multiplying a function by a constant, c, will shrink or stretch the function vertically. The graph of f(x) will shrink if the constant, c, is between 0 and 1 (0<=c<=1). And if c is greater than 1 then the function will stretch vertically. 
3. The above criterion should help you eliminate those statements that don't make sense. Hopefully this helps.