Question

Which of the following are true statements?

Check all that apply.

A. The graph of ƒ(x)=-1/2√x will look like the graph of ƒ(x)=√x but will reflect it about the x-axis and shrink it vertically by a factor of 1/2.
B. The graph of ƒ(x)=-1/2√x will look like the graph of ƒ(x)=√x but will shrink it horizontally by a factor of 1/2.
C. ƒ(x)=-1/2√x has the same domain but a different range as ƒ(x)=√x.
D. The graph of ƒ(x)=-1/2√x will look like the graph of ƒ(x)=√x but will shrink it vertically by a factor of 1/2.

Answer 1

Answer: A and C

Explanation:

edge 2022

Answer 2

Statements A and C are correct.

Explanation:

We have to select the true statements from the given four statements in options.

I think the statements A and C are true from the mathematical point of view.

If the original function is
`y = √(x)` and then by reflecting it about the x-axis the equation will become
`y = - √(x)`, and then shrinking it vertically by a factor of
`(1)/(2)` the function will finally become
`y = - (1)/(2) √(x)`.

Hence, statement A is true.

Again, the original function
`y = √(x)` has domain x ≥ 0 and range y ≥ 0, but in the transformed equation
`y = - (1)/(2) √(x)` has domain same as original equation i.e. x ≥ 0 but the range is different i.e. y ≤ 0.

Hence, statement C is also true. (Answer)