Q. 3 - Precalculus Enhanced with Graphing Utilities

Question

Suppose that the graph of a function $g$ is known. The graph of $y=g\left(x\right)+2$ may be obtained by a _______ shift of the graph of $g$ ________ a distance of $2$ units. 

Step-by-Step Solution

Answer

vertical; up

Step 1. Concept Used

If a positive real number $k$ is added to the outputs of a function $y=f\left(x\right)$, the graph of the new function $y=f\left(x\right)+k$ is the graph of $f$ shifted vertically up $k$ units.

If a positive real number $k$ is subtracted from the outputs of a function $y=f\left(x\right)$, the graph of the new function $y=f\left(x\right)-k$ is the graph of $f$ shifted vertically down $k$ units. 

Step 2. Fill in the blanks

As $2$ is added to the output of the known function $y=g\left(x\right)$, then the graph of the new function $y=g\left(x\right)+2$ is the graph of $g$ shifted vertically up $2$ units.

So the blanks are filled by vertical and up.