Answer:
[tex]g(x)=4(3)^{x+1}+8[/tex]
Step-by-step explanation:
Given:
The original function is given as:
[tex]f(x)=2(3)^{x+1}+4[/tex]
The above function is stretched vertically by a factor of 2 to form the graph of [tex]g(x)[/tex].
According to the rule of function transformations, when the graph of a function is stretched in the vertical direction by a factor of 'C', where, 'C' is a number greater than 1, then the function rule is given as:
[tex]f(x)\to Cf(x)[/tex]
Therefore, the function is multiplied by a factor of 'C' to get the equation of the stretched function.
Here, the the value of 'C' is 2. So, the equation of [tex]g(x)[/tex] is given as:
[tex]g(x)=2f(x)\\g(x)=2[2(3)^{x+1}+4]\\g(x)=4(3)^{x+1}+8[/tex]
Therefore, the equation of [tex]g(x)[/tex] is [tex]g(x)=4(3)^{x+1}+8[/tex].
