Question

Which statement correctly describes the relationship between the graph of f(x) and the graph of g(x)=f(x)+3

Answer 1

For this case we have:

Let a function of the form
`y = f (x)`,

By definition of function transformations we have:

Being
`k> 0`.

To graph
`y = f (x) + k`, the graph of f (x) k units must be moved upwards.

To graph
`y = f (x) -k`, the graph of f (x) k units must be moved down

In the given exercise we have:

`f (x)` and
`g (x) = f (x) +3`, that means that
`f (x)` was moved 3 units up, that is,
`k = 3`.

Answer:

The graph of
`g (x)` is the graph of
`f (x)` displaced three units up.