SOLUTION: Which of the following functions represents f(x) =8^x after a vertical compression by a factor of 1/4 and a reflection in the y-axis? g(x)=-1/4(8^x) g(x)=-(8^4x) g(x)=1/4(8^-

Algebra ->  Rational-functions -> SOLUTION: Which of the following functions represents f(x) =8^x after a vertical compression by a factor of 1/4 and a reflection in the y-axis? g(x)=-1/4(8^x) g(x)=-(8^4x) g(x)=1/4(8^-      Log On


   

Question 1139316: Which of the following functions represents f(x) =8^x after a vertical compression by a factor of 1/4 and a reflection in the y-axis?
g(x)=-1/4(8^x)
g(x)=-(8^4x)
g(x)=1/4(8^-x)
g(x)=8^-1/4x
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
A GENERAL NOTE: STRETCHES AND COMPRESSION OF THE PARENT FUNCTION
f%28x%29=b%5Ex
then the function f%28x%29=ab%5Ex+
-is stretched vertically by a factor of a if abs%28a%29%3E1
-is compressed vertically by a factor of a if abs%28a%29%3C1
-has a y-intercept at (0,a)
-has a horizontal asymptote of y=0, range of (0,infinity), and domain of (-infinity,infinity) which are all unchanged from the parent function
-when we multiply the parent function f%28x%29=b%5Ex by -1, we get a reflection about the x-axis.
-when we multiply the input by -1, we get a reflection about the y-axis

you are given:
f%28x%29+=8%5Ex
after a vertical compression by a factor of 1%2F4+ you got
g%28x%29+=%281%2F4%298%5Ex+
then multiply the input by -1 to get a reflection about the y-axis:
g%28x%29+=%281%2F4%298%5E%28-x+%29

=> your answer is: g%28x%29=%281%2F4%298%5E%28-x%29