Question

Explain how the range of a function $$\begin{gathered} y=f\left(x\right) \\ =x^2 \end{gathered}$$ compares to$$\begin{gathered} y=g\left(x\right) \\ =f\left(x\right)+k \end{gathered}$$

Short answer

The graph shifts vertically upward $k$units when $k>0$and $k<0$vertically downwards$k$units

Step-by-step solution

Given information

Given the equation $y=x^2$and

$y=f\left(x\right)+k$

Checking the effect of k

Here if$k>0$the graph shifts by$k$units vertically upward and$k$units vertically downward by$k$units for$k<0$