Answered

Which of the following are true statements?


Check all that apply.

AThe 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.
BThe 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.
Cƒ(x)=-1/2√x has the same domain but a different range as ƒ(x)=√x.
DThe 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.

...?

Verified Answer :

Answer:

A

C

Step-by-step explanation:

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Here we must compare a function and its transformation, we will see that the correct options are A and C.

First, we must define the transformations that we will be using here.

Reflection about the x-axis:

For a function f(x) a reflection about the x-axis is written as:

g(x) = -f(x)

Vertical contraction.

For a function f(x) a vertical contraction of scale factor k is written as:

g(x) = kf(x)

So here we start with:

ƒ(x)=√x

Then we reflect it about the x-axis to get:

ƒ(x)=-√x

Then we shrink it by a scale factor k = 1/2

ƒ(x) = (-1/2)√x

From this, we can see that the correct options are:

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.

And C is also true, because we have a reflection about the x-axis, the range changed from positive values to negative values, so:

C. ƒ(x)=-1/2√x has the same domain but a different range as ƒ(x)=√x.

Is also a correct option.

If you want to learn more, you can read:

https://brainly.com/question/14536884

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