For this case we have:
Let a function of the form [tex]y = f (x)[/tex],
By definition of function transformations we have:
Being [tex]k> 0[/tex].
To graph [tex]y = f (x) + k[/tex], the graph of f (x) k units must be moved upwards.
To graph[tex]y = f (x) -k[/tex], the graph of f (x) k units must be moved down
In the given exercise we have:
[tex]f (x)[/tex] and[tex]g (x) = f (x) +3[/tex], that means that[tex]f (x)[/tex] was moved 3 units up, that is, [tex]k = 3[/tex].
Answer:
The graph of [tex]g (x)[/tex] is the graph of[tex]f (x)[/tex] displaced three units up.
