Q. 97 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

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

Step 1: Given information

Given the equation $y=x^2$ and

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

Step 2: 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 $k<0$