Concept explainers
(a)
To show the shifts in graph with c = -3, -1,1 and 3.
(a)
Explanation of Solution
Given information: For each function sketch a graph on the same set of coordinate axes.
Graph:
Figure 1.
Figure 2.
Interpretation:
Interpretation of Figure 1.
We have modulus graph:-
we get :-
Values of c | Function |
-3 | |
-1 | |
1 | |
3 |
CaseI.
Using Vertical Shift in the graph,
So, the graph is drawn downward by three unit.
Case II.
Using Vertical Shift in the graph,
So, the graph is drawn downward by one unit.
Case III.
Using Vertical Shift in the graph,
So , the graph is drawn upward by one unit.
CaseIV.
Using Vertical Shift in the graph,
So, the graph is drawn upward by three units.
Interpretation of Figure 2.
We have modulus graph:-
we get :-
Value of c | Function |
-3 | |
-1 | |
1 | |
3 |
CaseI.
Using Vertical Shift in the graph,
So, the graph is drawn downward by three unit.
Case II.
Using Vertical Shift in the graph,
So, the graph is drawn downward by one unit.
Case III.
Using Vertical Shift in the graph,
So , the graph is drawn upward by one unit.
CaseIV.
Using Vertical Shift in the graph,
So, the graph is drawn upward by three units.
(b)
To sketch a graph of each function for c = -3, -1,1 and 3.
(b)
Explanation of Solution
Given information: For each function sketch a graph on the same set of coordinate axes.
Graph:
Figure 1.
Figure 2.
Interpretation:
Interpretation of Figure 1.
We have modulus graph:-
we get :-
Values of c | Function |
-3 | |
-1 | |
1 | |
3 |
Case I.
Using Horizontal Shift in the graph,
So , the graph is shifted towards right by three unit.
Case II.
Using Horizontal Shift in the graph,
So , the graph is shifted towards right by one unit.
CaseIII.
Using Horizontal Shift in the graph,
So, the graph is shifted towards left by one units.
CaseIV.
Using Horizontal Shift in the graph,
So, the graph is shifted towards left by three unit.
Interpretation of Figure 2.
We have modulus graph:-
we get :-
Value of c | Function |
-3 | |
-1 | |
1 | |
3 |
Case I.
Using Horizontal Shift in the graph,
So , the graph is shifted towards right by three unit.
Case II.
Using Horizontal Shift in the graph,
So , the graph is shifted towards right by one unit.
CaseIII.
Using Horizontal Shift in the graph,
So, the graph is shifted towards left by one units.
CaseIV.
Using Horizontal Shift in the graph,
So, the graph is shifted towards left by three unit.
Chapter 1 Solutions
EBK PRECALCULUS W/LIMITS
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning