Question

The function shown in the graph is shifted 4 units up to produce a new graph.

Answer 1

First of all, observe that the graphed function is $y=\sin(x)$.

Now, if we want to shift the graph 4 units up, it means that we want each point on the graph enlarge its y coordinate by 4: we no longer want to associate

$x\mapsto y$

but

$x\mapsto y+4$

And since $y=f(x)$, we want to map

$x\mapsto f(x)+4$

And in our case, $f(x)=\sin(x)$, so the answer is

$\sin(x)+4$