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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.

Respuesta :

Answer:

Statements A and C are correct.

Step-by-step 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 [tex]y = \sqrt{x}[/tex] and then by reflecting it about the x-axis the equation will become [tex]y = - \sqrt{x}[/tex], and then shrinking it vertically by a factor of [tex]\frac{1}{2}[/tex] the function will finally become [tex]y = - \frac{1}{2} \sqrt{x}[/tex].

Hence, statement A is true.

Again, the original function [tex]y = \sqrt{x}[/tex] has domain x ≥ 0 and range y ≥ 0, but in the transformed equation [tex]y = - \frac{1}{2} \sqrt{x}[/tex] 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)

Answer: A and C

Step-by-step explanation:

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