Answer: B. function h is a reflection and a dilation of function f
Step-by-step explanation:
- A reflection gives the mirror image of function.
- A function can be reflected about an axis by multiplying by -1.
- To reflect function about the x-axis, multiply f(x) by -1 to get -f(x).
Also, dilation provides either vertical or horizontal stretch or compression.
It uses a scale factor k to multiply the function such that new function will be kf(x).
Here, [tex]f(x)=2^x[/tex] and [tex]h(x)= -3\times 2^x[/tex]
We can write h(x) as
[tex]h(x)=(-1) \times (3) \times (2^x)=(-1) \times (3) \times f(x)[/tex]
So here scale factor =3 and -1 gives it a reflection.
So, the correct statement would be B. function h is a reflection and a dilation of function f.
