Wich graph is the result of the reflection f(x) =1/4(8)^x across the y axis and then across the x- axis

Answer:

I assume that the function is:

[tex]f(x) = \frac{1}{4}*8^x[/tex]

Now let's describe the general transformations that we need to use in this problem.

Reflection across the x-axis:

For a general function f(x), a reflection across the x-axis is written as:

g(x) = -f(x)

Reflection across the y-axis:

For a general function f(x), a reflection across the y-axis is written as:

g(x) = f(-x)

Then a reflection across the y-axis, and then a reflection across the x-axis is just:

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

In this case, we have:

[tex]f(x) = \frac{1}{4}*8^x[/tex]

then:

[tex]g(x) = -f(-x) = -\frac{1}{4}*8^{-x}[/tex]

Now we can graph this, to get the graph you can see below:

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