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) = k*f(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
