Question

which function g represents the exponential function f(x)=3^x after a horizontal stretch by a factor of 4 and a reflection across the y-axis?

Answer 1

Answer: h(x) = 3^(-x/4)

Explanation:

If we have a function f(x), an horizontal stretch of scale factor k is written as:

g(x) = f(x/k)

So, if we have the function f(x) = 3^x

A horizontal stretch of scale factor 4 is:

g(x) = f(x/4) = 3^(x/4)

Now we have a reflection across the y-axis

If we have a function f(x), a reflection across the x-axis is written as:

g(x) = f(-x)

Then if now we apply a reflection across the y-axis to the function g(x), we have:

h(x) = g(-x) = 3^(-x/4)

Then the transformation that we wanted is:

h(x) = 3^(-x/4)