Chapter 2.5, Problem 3AYU

To determine

To fill:The term used to define the transformation for the graph $y=g\left(x\right)+2$ from the graph $y=f\left(x\right)$ .

Answer to Problem 3AYU

The graph of $y=g\left(x\right)+2$ is obtained by averticalshift of graph of $y=f\left(x\right)$ to the upward at a distance 2 units.

Explanation of Solution

For $c>0$ .

  $h\left(x\right)=f\left(x\right)+c$ shifts the graph of $f\left(x\right)$ vertically upward by $c$ units,

  $h\left(x\right)=f\left(x\right)–c$ shifts the graph of $f\left(x\right)$ vertically downward by $c$ units,

  $h\left(x\right)=f\left(x+c\right)$ shifts the graph of $f\left(x\right)$ horizontally left by $c$ units,

  $h\left(x\right)=f\left(x–c\right)$ shifts the graph of $f\left(x\right)$ horizontally right by $c$ units.

Now, consider the graph of $y=g\left(x\right)+2$ .

Here, the graph is of the form $h\left(x\right)=f\left(x\right)+c$ ,

So, $c=2$

The graph of $y=g\left(x\right)+2$ can be obtained by a vertical shift of graph of $y=f\left(x\right)$ to the upward at a distance 2 units.