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