Chapter 1.7, Problem 6E

(a)

To determine

To sketch a graph of each function forc = -3, -1, 1 and 3.

Explanation of Solution

Given information: For each function sketch a graph on the same set of coordinate axes.

Graph:

  

Interpretation: We have modulus graph:- $y=\sqrt{x}$ . Now putting values of c in function

  $y=\sqrt{x}+c$ we get :-

Values of c	Function
-3	$y=\sqrt{x}-3$
-1	$y=\sqrt{x}-1$
1	$y=\sqrt{x}+1$
3	$y=\sqrt{x}+3$

CaseI. $y=\sqrt{x}-3$

The Vertical Shift in the graph, $y=f(x)$ is represented as :-

  $h(x)=f(x)-c$ which implies vertical shift c units down.

So, the graph of function $y=\sqrt{x}-3$ is drawn downward by three unit.

CaseII. $y=\sqrt{x}-1$

The Vertical Shift in the graph, $y=f(x)$ is represented as :-

  $h(x)=f(x)-c$ which implies vertical shift c units down.

So, the graph is drawn downward by one unit.

Case III. $y=\sqrt{x}+1$

The Vertical Shift in the graph, $y=f(x)$ is represented as :-

  $h(x)=f(x)+c$ which implies vertical shift c units up.

So , the graph with function $y=\sqrt{x}+1$ is drawn upward by one unit.

CaseIV. $y=\sqrt{x}+3$

The Vertical Shift in the graph, $y=f(x)$ is represented as :-

  $h(x)=f(x)+c$ which implies vertical shift c units up.

So, the graph with function $y=\sqrt{x}+3$ is drawn upward by three units.

(b)

To determine

To show the shifts in graph with c = -3,-1, 1 and 3.

Explanation of Solution

Given information: For each function sketch a graph on the same set of coordinate axes.

Graph:

  

Interpretation: We have modulus graph:- $y=\sqrt{x}$ . Now putting values of c in function $y=\sqrt{x-c}$ we get :-

Values of c	Function
-3	$y=\sqrt{x+3}$
-1	$y=\sqrt{x+1}$
1	$y=\sqrt{x-1}$
3	$y=\sqrt{x-3}$

CaseI. $y=\sqrt{x+3}$

The HorizontalShift in the graph, $y=f(x)$ is represented as :-

  $h(x)=f(x)+c$ which implies horizontal shift c units to the left .

So, the graph with function $y=\sqrt{x}+3$ is shifted towards left by three unit.

CaseII. $y=\sqrt{x+1}$

The Horizontal Shift in the graph, $y=f(x)$ is represented as :-

  $h(x)=f(x)+c$ which implies horizontal shift c units to the left.

So, the graph of function $y=\sqrt{x+1}$ is shifted towards left by one units.

Case III. $y=\sqrt{x-1}$

The Horizontal Shift in the graph, $y=f(x)$ is represented as :-

  $h(x)=f(x)-c$ which implies horizontal shift c units to the right.

So , the graph with function $y=\sqrt{x-1}$ is shifted towards right by one unit.

Case IV. $y=\sqrt{x-3}$

The Horizontal Shift in the graph, $y=f(x)$ is represented as :-

  $h(x)=f(x)-c$ which implies horizontal shift c units to the right.

So , the graph with function $y=\sqrt{x-3}$ is shifted towards right by three unit.