Chapter 6.8, Problem 58PPSE

Solution

a.

To draw the graph for the given expression.

Given:

The given expressionsare:

  $\begin{array}{l}y=\sqrt{-x}\\ y=\sqrt{1-x}\\ y=\sqrt{2-x}\end{array}$

Graph:

The parent function of all the functions is $y=\sqrt{x}$ . First reflect the graph of the parent function about y-axis to get the graph of $y=\sqrt{-x}$ . Then shift the resulting graph first by 1 unit to the left and then by 2 units to the left to get graphs of $y=\sqrt{1-x}$ and $y=\sqrt{2-x}$ as shown below.

  

b.

To explain the difference between the graphs of the given functions.

Given:

The given expressions are:

  $\begin{array}{l}y=\sqrt{h-x}\\ y=\sqrt{x-h}\end{array}$

Explanation:The graph of the function $y=\sqrt{x-h}$ is obtained by shifting the parent function $y=\sqrt{x}$ to the right by $h$ units, and the graph of the function $y=\sqrt{h-x}$ is obtained by reflecting the graph of the parent function $y=\sqrt{x}$ about y-axis and then shifting right by $h$ units.