Concept explainers
In Problems 25-32, the graph of a function is given. Use the graph to find:
a. The intercepts, if any
b. The domain and range
c. The intervals on which the function is increasing, decreasing, or constant
d. Whether the function is even, odd, or neither
25.
To find: The following values using the given graph:
a. Intercepts ().
Answer to Problem 21AYU
From the graph, concluding the following results:
a. Intercepts ()
.
Explanation of Solution
Given:
It is asked to find the intercepts ( and if any), domain and range, increasing intervals, decreasing intervals, and constant intervals of the function using the graph. Also, check whether the function is even, odd or neither.
Graph:
Interpretation:
a. Intercepts (): The points, if any, at which a graph crosses or touches the coordinate axes are called the intercepts.
The of a point at which the graph crosses or touches the is an , and the of a point at which the graph crosses or touches the is an .
The intercepts of the graph are the points and .
The are and 2; the is 3.
To find: The following values using the given graph:
b. The domain and range set of the function.
Answer to Problem 21AYU
From the graph, concluding the following results:
b. The domain and range set of the function.
The domain of is or the interval .
The range of is or the interval .
Explanation of Solution
Given:
It is asked to find the intercepts ( and if any), domain and range, increasing intervals, decreasing intervals, and constant intervals of the function using the graph. Also, check whether the function is even, odd or neither.
Graph:
Interpretation:
b. The domain and range set of the function.
To determine the domain of notice that the points on the graph of have between to 4, inclusive; and for each number between to 4, there is a point on the graph. The domain of is or the interval .
The points on the graph all have between 0 and 3, inclusive; and for each such number , there is at least one number in the domain. The range of is or the interval .
To find: The following values using the given graph:
c. Increasing intervals, decreasing intervals and constant interval if any.
Answer to Problem 21AYU
From the graph, concluding the following results:
c. The function and the function is . There is no constant interval in the given graph.
Explanation of Solution
Given:
It is asked to find the intercepts ( and if any), domain and range, increasing intervals, decreasing intervals, and constant intervals of the function using the graph. Also, check whether the function is even, odd or neither.
Graph:
Interpretation:
c. Increasing intervals, decreasing intervals and constant interval if any.
It can be directly concluded from the graph that the curve is decreasing from to , then increasing from to 0, then decreasing from 0 to 2, and at last it is increasing from 2 to 4.
Therefore, the function is increasing in the intervals and and the function is decreasing in the intervals and . There is no constant interval in the given graph.
To find: The following values using the given graph:
d. Nature of the function (even, odd or neither).
Answer to Problem 21AYU
From the graph, concluding the following results:
d. The given function is an even function.
Explanation of Solution
Given:
It is asked to find the intercepts ( and if any), domain and range, increasing intervals, decreasing intervals, and constant intervals of the function using the graph. Also, check whether the function is even, odd or neither.
Graph:
Interpretation:
d. Nature of the function (even, odd or neither).
By the theorem of test for symmetry, “A function is even if and only if its graph is symmetric with respect to the . A function is odd if and only if its graph is symmetric with respect to the origin”.
As the given graph is symmetric with respect to , the function is even.
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
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University Calculus: Early Transcendentals (3rd Edition)
Glencoe Math Accelerated, Student Edition
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Calculus & Its Applications (14th Edition)
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