Question

Function is a transformation of the parent exponential function


`f(x) = 2^(x).h(x) = - 3 * {2}^(x)`


Which statement is true?

A. Function h is a reflection and a translation of function f

B. function h is a reflection and a dilation of function f

C. function h is a horizontal translation of function f

D. function h is a vertical translation of function f ​

Answer 1

Answer: B. function h is a reflection and a dilation of function f

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,
`f(x)=2^x` and
`h(x)= -3* 2^x`

We can write h(x) as

`h(x)=(-1) * (3) * (2^x)=(-1) * (3) * f(x)`

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.