# Which graph is the result of reflecting f(x) = (8)x across the y-axis and then across the x-axis?

###### Question:

## Answers

Refrection of a function across the y-axis, changes the sign of x in the function.

Thus, given the function:

[tex]f(x)=(8)^x[/tex]

Refrection of the function across the y-axis will result in the function:

[tex]g(x)=(8)^{-x}[/tex]

Refrecting a function across the x-axis, changes the sign of the function.

Thus, refrecting the function:

[tex]g(x)=(8)^{-x}[/tex]

across the x-axis will result in the function:

[tex]h(x)=-(8)^{-x}[/tex]

The graph of [tex]f(x)=(8)^x[/tex] and [tex]h(x)=-(8)^{-x}[/tex] is attached.

The green curve represents the graph of the function [tex]f(x)=(8)^x[/tex], while the orange curve represents the graph of the function [tex]h(x)=-(8)^{-x}[/tex].

[tex]Which graph is the result of reflecting f(x) = (8)x across the y-axis and then across the x-axis?[/tex]

The answer is D. A is f(x) =1/4 (8)x

Step-by-step explanation:

Assuming yo mean f(x)=8ˣ

to reflect the function across the y axis, multiply every x by -1

to reflect the function across x axis, multiply the whole function by -1

see attachment for graphs

red=original line

so across y axis would be

f(x)=(8)⁻ˣ

this is the blue line

reflection across x axis then would be

f(x)=-1(8)⁻ˣ

this is the green line

so the resulting graph is the green line

[tex]Which graph is the result of reflecting f(x) = (8)x across the y-axis and then across the x-axis?[/tex]

Check the picture below.

[tex]Which graph is the result of reflecting f(x) = (8)x across the y-axis and then across the x-axis?[/tex]