MATH SOLVE

4 months ago

Q:
# Let f(x)=6(2)x−1+4 . The graph of f(x) is stretched vertically by a factor of 4 to form the graph of g(x) . What is the equation of g(x)g(x) ? Enter your answer in the box. g(x) =

Accepted Solution

A:

Answer:[tex]g(x)=24(2)^{x-1}+16[/tex]

Step-by-step explanation: Given function [tex]f(x)=6(2)^{x-1}+4[/tex].We need to find the function that would be stretched vertically by a factor of 4 , that will result function g(x).According to rules of transformation : y =C f(x), function f(x) stretched vertically by a factor of C.According to problem, we need to stretched vertically by a factor of 4.So, we need to multiply given function f(x) by 4.On multiplying function by 4, we get [tex]g(x)=4[6(2)^{x-1}+4][/tex]On distributing 4 over parenthesis, we get [tex]g(x)=24(2)^{x-1}+16[/tex]Therefore, [tex]g(x)=24(2)^{x-1}+16[/tex]

Step-by-step explanation: Given function [tex]f(x)=6(2)^{x-1}+4[/tex].We need to find the function that would be stretched vertically by a factor of 4 , that will result function g(x).According to rules of transformation : y =C f(x), function f(x) stretched vertically by a factor of C.According to problem, we need to stretched vertically by a factor of 4.So, we need to multiply given function f(x) by 4.On multiplying function by 4, we get [tex]g(x)=4[6(2)^{x-1}+4][/tex]On distributing 4 over parenthesis, we get [tex]g(x)=24(2)^{x-1}+16[/tex]Therefore, [tex]g(x)=24(2)^{x-1}+16[/tex]