To find: An expression function for the graph which satisfies the given conditions.
Answer to Problem 18RE
Solution:
The equation of the function is
Explanation of Solution
Given:
The graph has a line segment connecting (−2, 2) and (−1, 0) and it consist a top half of the circle with centre (0, 0) and radius 1.
Calculation:
Find the slope of the line segment joining the points (−2, 2) and (−1, 0) as follows.
Thus, the slope of the line segment is
Find the y-intercept of the line segment joining the points (−2, 2) and (−1, 0) as follows.
Thus, y-intercept is
Therefore, the equation of the line segment is,
Also there exist top half of the circle with centre (0, 0) and radius 1.
The standard equation of the circle which passes through the (0, 0) and radius 1 is
Solve the equation for y as follows.
Since the graph consist only top half of the circle, consider only the positive root. That is
Therefore, equation of the top half of the circle is
Combine the equations (1) and (2), the function of the graph is
Chapter 1 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- 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