Question

The graph of f and g are given. Find a formula for the function g.

Short answer

$g\left(x\right)=x^3+3$

Step-by-step solution

Step 1. Concept of vertical shift.

Adding a constant to a function shifts the graph upward or downward if the constant is positive or negative respectively.

Step 2. Given condition.

Given equation is

$f\left(x\right)=x^3$; And the graph of $g\left(x\right)$is

Step 3. Determining the formula for the function g.

The graph shifts upward by the 3 units,

So,$$\begin{gathered} c=3 \\ g\left(x\right)=x^3+3 \end{gathered}$$