SOLUTION: The graph of f(x) = 1/ 3^- x is reflected about the y-axis and compressed vertically by a factor of 1/4. What is the equation of the new function, g(x)? *I thought the ans

Algebra ->  Functions -> SOLUTION: The graph of f(x) = 1/ 3^- x is reflected about the y-axis and compressed vertically by a factor of 1/4. What is the equation of the new function, g(x)? *I thought the ans      Log On


   

Question 1128744: The graph of
f(x) = 1/ 3^- x is reflected about the y-axis and compressed vertically by a factor of 1/4.
What is the equation of the new function, g(x)?
*I thought the answer would be 1/4 (x-1/3^-x), assuming that the vertical compression variable goes outside of the parentheses and 1/3^x-3 goes inside the equation. This however was wrong. Can someone explain how setting up these types of equations should be done, especially for future references? Thanks.
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Here are the plots of{
(1) +f%28x%29+=+1%2F%28+3%5E%28-x%29%29+ and
(2) +f%28x%29+=+1%2F%28+3%5Ex+%29+

---------------------------
For vertical compression, previous values of
+x+ are larger to make up for the factor of +4+ I will put in
+f%28x%29+=+1%2F%28+3%5E%284X%29+%29+. Here's the plot:
+graph%28+400%2C+400%2C+-5%2C+5%2C+-10%2C+10%2C+1%2F%28+3%5E%284x%29%29+%29+
I think this is right. Get another opinion also

Answer by greenestamps(13350) About Me  (Show Source):
You can put this solution on YOUR website!


To begin with, the given function is in a very unusual form.

1%2F%283%5E%28-x%29%29+=+3%5Ex

But we can, nevertheless, work the problem with the function as given.

The vertical compression factor becomes a factor outside the parentheses, as you say.

But what you are doing with the reflection about the y axis makes no sense. Reflecting a function about the y axis changes x to the opposite of x.

So a reflection of f(x) = 1/3^(-x) about the y axis and a compression vertically by a factor of 1/4 yields

g(x) = (1/4)(1/(3^x))

Graphs of f(x) (red) and g(x) (green):