Question

Which function represents g(x), a reflection of f(x) = 4(one-half) Superscript x across the x-axis?

g(x) = −4(2)x
g(x) = 4(2)−x
g(x) = −4(one-half) Superscript x
g(x) = 4(one-half) Superscript negative x

Answer 1

Explanation:

we have

we know that

The rule of the reflection across the x-axis is

(x,f(x)) ------> (x,-f(x))

therefore

g(x) = −4(one-half) Superscript x

see the attached figure to better understand the problem

Answer 2

`g(x)=-4((1)/(2))^(x)`

Explanation:

we have

`f(x)=4((1)/(2))^(x)`

we know that

The rule of the reflection across the x-axis is

(x,f(x)) ------> (x,-f(x))

therefore

`g(x)=-f(x)`

`g(x)=-4((1)/(2))^(x)`

g(x) = −4(one-half) Superscript x

see the attached figure to better understand the problem