To identify the parent function for the given graph, write the equation and describe the transformation for the graph.
Answer to Problem 32E
The equation is:
The parent function is:
Explanation of Solution
Given:
The given graph is:
After looking at the graph the following can be concluded:
The given graph is transformation of
x -intercept: The graph intersects the x -axis at about
y- intercept: The graph intersects the y- axis at about (0,2), hence the x- intercept is about 2.
Equation:
To write the equation of the given graph the standard form is used which is:
Here,
a is x- intercept of the given graph.
Substituting the value of a into the equation (i),
Hence, the obtained equation is:
Verification:
Using the graphing tool the equation is plotted:
When the plotted graph and given graph are compared, it is found that both the graphs are equal, which means that the obtained equation is correct.
Parent function:
The obtained equation is:
Therefore, the function is:
Hence, the parent function is:
Transformation Interpretation:
The function is
Calculation for graph:
Consider
Values of x | Values of f (x ) |
0 | 2 |
-1 | 1 |
1 | 3 |
2 | 4 |
-3 | 1 |
Using the above table the graph can be plotted.
Calculation for graph:
Consider
Values of x | Values of g (x ) |
1 | 1 |
-1 | 1 |
2 | 2 |
-2 | 2 |
3 | 3 |
Using the above table the graph can be plotted.
Graph:
Hence, by comparing
The parent function is
Conclusion:
The obtained equation is
Chapter 1 Solutions
EBK PRECALCULUS W/LIMITS:GRAPH.APPROACH
- 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