SOLUTION: Can someone explain how to solve this problem? The graph of f(x) = 1/4^ −x is reflected about the y-axis and compressed vertically by a factor of 1/5. What is the equatio

Algebra ->  Graphs -> SOLUTION: Can someone explain how to solve this problem? The graph of f(x) = 1/4^ −x is reflected about the y-axis and compressed vertically by a factor of 1/5. What is the equatio      Log On


   



Question 1137988: Can someone explain how to solve this problem?
The graph of
f(x) = 1/4^ −x is reflected about the y-axis and compressed vertically by a factor of
1/5.
What is the equation of the new function, g(x)?

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The graph of
f%28x%29+=+%281%2F4%29%5E+%28-x%29+is reflected about the y-axis and compressed vertically by a factor of
1%2F5.
What is the equation of the new function, g%28x%29?
The basic parent function of any exponential function is f%28x%29+=+b%5Ex, where b is the base.
Because an exponential function is simply a function, you can transform the parent graph of an exponential function in the same way as any other function:
f%28x%29+=a%2A+b%5E%28x-h%29+%2Bk+
where a is the vertical transformation,+h is the horizontal shift, and k is the vertical shift.

in your case given 1%2F5 is value of a, so
g%28x%29=%281%2F5%29%281%2F4%29%5E+%28-x%29