Chapter 1.7, Problem 6E

(a)

To determine

To sketch: the graphs of the function when $c=-3,-2,2$ and 3 on the same set of coordinate axes.

Explanation of Solution

Given information:

Given function

  $f\left(x\right)=\sqrt{x}+c$

Calculation:

The function is $f\left(x\right)=\sqrt{x}+c$ , when $c=-3$ , then the function is $f\left(x\right)=\sqrt{x}-3$ . The parent graph is $g\left(x\right)=\sqrt{x}$ So, $f\left(x\right)$ is obtained by shifting the graph of $g\left(x\right)$ down three units.

When $c=-2$ , then the function is $f\left(x\right)=\sqrt{x}-2$ . The parent graph is $g\left(x\right)=\sqrt{x}$ So, $f\left(x\right)$ is obtained by shifting the graph of $g\left(x\right)$ down two units.

When $c=2$ , then the function is $f\left(x\right)=\sqrt{x}+2$ . The parent graph is $g\left(x\right)=\sqrt{x}$ So, $f\left(x\right)$ is obtained by shifting the graph of $g\left(x\right)$ up two units.

When $c=3$ , then the function is $f\left(x\right)=\sqrt{x}+3$ . The parent graph is $g\left(x\right)=\sqrt{x}$ So, $f\left(x\right)$ is obtained by shifting the graph of $g\left(x\right)$ up three units.

The graph:

  

(b)

To determine

To sketch: the graphs of the function when $c=-3,-2,2$ and 3 on the same set of coordinate axes.

Explanation of Solution

Given information:

Given function

  $f\left(x\right)=\sqrt{x-c}$

Calculation:

The function is $f\left(x\right)=\sqrt{x-c}$ , when $c=-3$ then the function is

  $f\left(x\right)=\sqrt{x-\left(-3\right)}$ Or $\sqrt{x+3}$ . The parent graph is $g\left(x\right)=\sqrt{x}$ So, $f\left(x\right)$ is obtained by shifting the graph of $g\left(x\right)$ three units left.

When $c=-2$ , then the function is $f\left(x\right)=\sqrt{x-\left(-2\right)}$ or $\sqrt{x+2}$ . The parent graph is $g\left(x\right)=\sqrt{x}$ So, $f\left(x\right)$ is obtained by shifting the graph of $g\left(x\right)$ two units left.

When $c=2$ , then the function is $f\left(x\right)=\sqrt{x-2}$ . The parent graph is $g\left(x\right)=\sqrt{x}$ So, $f\left(x\right)$ is obtained by shifting the graph of $g\left(x\right)$ two unit right.

When $c=3$ , then the function is $f\left(x\right)=\sqrt{x-3}$ . The parent graph is $g\left(x\right)=\sqrt{x}$ So, $f\left(x\right)$ is obtained by shifting the graph of $g\left(x\right)$ three units right.

The graph: