Concept explainers
a)
To write: An equation that can be solved to find the points of intersection of the graphs of
An equation that can be solved to find the points of intersection of the graphs of
Given Information:
The equations
Concept Used:
The points of intersection of graphs of
Calculation:
Equate
Therefore,
b)
To find: Write an equation that can be solved to find the x -intercepts of the graph of y .
The required equation is
Given Information:
The equation
Concept Used:
The intercept for any equation is found by equation it to 0.
Calculation:
Equate
Therefore, the required equation is
c)
To explain: How does the graphical model reflect the fact that the answers to (a) and (b) are equivalent algebraically.
Given Information:
The equations
Figure 1
Explanation:
Draw the vertical lines at the points of intersection of
Figure 2
From figure 2 it follows that the value of
Also, the equation for finding the intersection points of
Therefore, the graphical model reflects the fact that the answers to (a) and (b) are equivalent algebraically.
d)
To check: Numerically that the
Given Information:
The equations
Calculation:
The equation
The graph of
Figure 3
Thus, the real solutions of
Now, substitute
Now, substitute
Thus,
Therefore, it follows that the intercepts of
Chapter 1 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning