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Concept explainers
The graph of a function f is given.
(a) State the value of f(1).
(b) Estimate the value of f(‒1).
(c) For what values of x is f(x) = 1?
(d) Estimate the value of x such that f(x) = 0.
(e) State the domain and range of f.
(f) On what interval is f increasing?
(a)
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The value of
Answer to Problem 1E
The value of
Explanation of Solution
Given:
Plot the points in the given graph as shown below in Figure 1.
Calculation:
In Figure.1, x-axis represents the values of x, and y-axis represents the values of
From Figure 1, it is noticeable that the point (1, 3) is plotted.
Therefore, the value of
(b)
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The value of
Answer to Problem 1E
The value of
Explanation of Solution
From Figure 1, it is seen that when x = −1 the f(x) is approximately equal to −0.2.
Therefore, the value of
(c)
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The value of x if
Answer to Problem 1E
If
Explanation of Solution
From Figure 1, it is it is noticeable that the points (0, 1) and (3, 1) are plotted.
Therefore, when
(d)
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The value of x if
Answer to Problem 1E
If
Explanation of Solution
It is seen from the Figure 1 that when f(x) = 0, the value of x is approximately −0.8.
Therefore, when
(e)
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The domain and range of f.
Answer to Problem 1E
The domain of f is
Explanation of Solution
Since, the domain of a function is the set of all x values of the graph, the domain is
Since, the range of a function is the set of all y values of the graph, the range of the function is
(f)
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The increasing interval of f.
Answer to Problem 1E
The increasing interval of f is
Explanation of Solution
From Figure 1, it is noticeable that the curve is increasing between
Therefore, the increasing interval of f is
Chapter 1 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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