Concept explainers
Use the graph of the function shown to find:
(a) The domain and the range of .
(b) The intervals on which is increasing, decreasing, or constant.
(c) The
(d) The absolute maximum and absolute minimum.
(e) Whether the graph is symmetric with respect to the , the , or the origin.
(f) Whether the function is even, odd, or neither.
(g) The intercepts, if any.
To find:
a. The domain and the range of .
Answer to Problem 17RE
Solution:
a. .
Explanation of Solution
Given:
Calculation:
a. Domain: set of all the values of for which graph is defined.
Hence domain .
Range: set of all the values of for which graph is defined.
Hence Range .
To find:
b. The intervals on which is increasing, decreasing, or constant.
Answer to Problem 17RE
Solution:
b. The function is increasing in the interval .
The function is decreasing in the interval .
The function is not constant on any interval.
Explanation of Solution
Given:
Calculation:
b. From the graph we see that, the function is increasing in the interval and that is .
The function is decreasing in the interval .
The function is not constant on any interval.
To find:
c. The local minimum values and local maximum values.
Answer to Problem 17RE
Solution:
c. local maximum value is and . There is no Local minimum.
Explanation of Solution
Given:
Calculation:
c. Local maximum exists at and the local maximum value is .
Local maximum exists at and the local maximum value is .
The graph does not have local minimum.
To find:
d. The absolute maximum and absolute minimum.
Answer to Problem 17RE
Solution:
d. The graph has absolute maximum at and it does not have absolute minimum.
Explanation of Solution
Given:
Calculation:
d. The graph has absolute maximum at and it does not have absolute minimum.
To find:
e. Whether the graph is symmetric with respect to the , the , or the origin.
Answer to Problem 17RE
Solution:
e. The Graph is not symmetric with respect to the , the , or the origin.
Explanation of Solution
Given:
Calculation:
e. The Graph is not symmetric with respect to the , the , or the origin.
To find:
f. Whether the function is even, odd, or neither.
Answer to Problem 17RE
Solution:
f. The function is neither even nor odd.
Explanation of Solution
Given:
Calculation:
f. From , we see that the graph is not symmetric with respect to the , the or origin. Therefore, the function is neither even nor odd.
To find:
g. The intercepts, if any.
Answer to Problem 17RE
Solution:
g. .
.
Explanation of Solution
Given:
Calculation:
g. are those where the graph meets or has 0, .
are those where the graph meets or has 0,.
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
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