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.

Short answer

vertical; up

Step-by-step solution

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.