Question

The function f(x) = 0.11(3)x is reflected over the x-axis to produce function g(x). Function g(x) is then reflected over the y-axis to produce function h(x). Which function represents h(x)?

a. h(x) = –0.11(3)x
b. h(x) = 0.11(3)–x
c. h(x) = 0.11(3)x
d. h(x) = –0.11(3)–x

Answer 1

the answer is:

D) h(x)= -0.11(3)-x

Hope, this helps

(E2020)

Answer 2

Option d is correct

`h(x) = -0.11 \cdot (3)^(-x)`

Explanation:

Given the function:

`f(x) = 0.11 \cdot 3^x`

First find the function g(x) when f(x) is reflected over the x-axis.

The rule of reflection across x-axis is given by:

`(x, y) \rightarrow (x, -y)`

then;

Apply the rule of reflection across x-axis on f(x) we get,

`g(x)=-0.11 \cdot (3)^(x)`

Now, function g(x) is then reflected over the y-axis to produce function h(x).

The rule of reflection across y-axis is given by:

`(x, y) \rightarrow (-x, y)`

then;

Apply the rule of reflection across y-axis on g(x) we get,

`h(x) = -0.11 \cdot (3)^(-x)`

Therefore,
`h(x) = -0.11 \cdot (3)^(-x)` function represents h(x)