Respuesta :

apologiabiology
a reflection across the x axis means times the whole thing by -1
reflect across y axis  means multiply every x by -1

so we got
from f(x)=2x
a reflection across either axis results in f(x)=-2x
but wat
why we have exponents

I pick the last option, h(x)=2^-x

Answer: [tex]h(x) = 2^{-x}[/tex]

Step-by-step explanation:

Here the given function is,

[tex]f(x) = 2^x[/tex]

Let (x,y) are the coordinates of the above exponential function,

By the rule of reflection about x-axis,

[tex](x,y)\rightarrow (-x,-y)[/tex]

Thus, in the transformed figure that is obtained after the reflection about x-axis,

x is replaced by -x and y is replaced by -y,

Let h(x) = - f(x)

Hence, the transformed figure is,

[tex]h(x) = 2^{-x}[/tex]

⇒ Last Option is correct.