SOLUTION: Let g(x)=2(4)^x+3 - 5. a) describe the function as a transformation of f(x)=4^x. b) graph the function using your knowledge of transformations. c) what is the horizontal asympto

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Let g(x)=2(4)^x+3 - 5. a) describe the function as a transformation of f(x)=4^x. b) graph the function using your knowledge of transformations. c) what is the horizontal asympto      Log On


   

Question 1012179: Let g(x)=2(4)^x+3 - 5.
a) describe the function as a transformation of f(x)=4^x.
b) graph the function using your knowledge of transformations.
c) what is the horizontal asymptote of the graph of g?
Answer by FormerJosephStalin(2) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there!
Thanks for the question.
So we are given the exponential function y=2%284%29%5E%28x%2B3%29+-+5. Since a = 2, the graph is compressed. Since the graph has an exponent of x + 3 and a vertical shift of -5. The graph of y=4%5Ex will be shifted to the left 3 units and down 5. I apologize for the lack of graphics. It is difficult to upload media on here. But you can look at desmos.com. Now, since y=4^x or any exponential function with no vertical shift has an asymptote of y =0, the asymptote will be shifted down 5 units to y = -5.
Hope this helped! :)