Answer: Option C
Step-by-step explanation:
If the graph of the function [tex]g(x)=f(x) +b[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]b> 0[/tex] the graph moves vertically upwards.
If [tex]b <0[/tex] the graph moves vertically down
In this problem we have the function [tex]g(x)=e^x+5[/tex] and our parent function is [tex]f(x) = e^x[/tex]
therefore it is true that [tex]b =5 > 0[/tex]
Therefore the graph of [tex]f(x)=e^x[/tex] is moves vertically upwards by a factor of 5 units.
The answer is the Option C: "The graph of g(x) is the graph of f(x) shifted up 5 units"
