Answer: [tex]g(x)=3^x+2[/tex]
Step-by-step explanation:
The function [tex]f(x)=3^x[/tex] is an exponential function of base 3.
This function has the point of intersection with the y-axis at [tex]y=1[/tex].
And in the point [tex]x=1[/tex] the value of the function is 3.
In the grph you can observe an exponential function that cuts the y-axis at the point [tex]y=3[/tex] and when [tex]x=1[/tex], then [tex]g(x)=5[/tex].
Therefore, the function g(x) is the function f(x) shifted two units up.
Then, the transfomration for f(x) is:
[tex]g(x)=f(x)+2[/tex]
Therefore, the equation g(x) is:
[tex]g(x)=3^x+2[/tex]
