Chapter ISG, Problem 9.2.7P

To determine

To calculate the shift in graph

Answer to Problem 9.2.7P

The graph shifts vertically by 1 unit downward from original position.

Explanation of Solution

Given Information: $h\left(x\right)={\left(\frac{1}{2}x\right)}^2$ and $g\left(x\right)={\left(\frac{1}{2}x\right)}^2-3$

Formula Used: Graphing Utility

Calculation:

For such equations, a graphing utility can often be used to investigate possible solutions. When a graphing utility is used to solve an equation, usually approximate solutions are obtained.

•   $h\left(x\right)={\left(\frac{1}{2}x\right)}^2$

Put the value of $x$ in $h\left(x\right)$ , get:

$x$	-2	-1	0	1	2
$h\left(x\right)$	1	0.25	0	0.25	1

  $g\left(x\right)={\left(\frac{1}{2}x\right)}^2-3$

Put the value of $x$ in $h\left(x\right)$ , get:

$x$	-2	-1	0	1	2
$g\left(x\right)$	-2	-2.75	-3	-2.75	-2

  

The graph shifts vertically by 1 unit downward from original position.