When we have a function f and we want to move it up or down we must add something to the function. If we add a positive number it will move the graph up, if we subtract it will move the graph down.
We want to move up the following graph:
[tex]f(x)=x^3[/tex]If we want to move it up we must add a positive number to the function. We want 4 units up then let's add 4 to the function
[tex]f(x)=x^3\Rightarrow g(x)=x^3+4[/tex]Then the function that represents that transformation is
[tex]g(x)=x^3+4[/tex]