BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.1, Problem 1E

(a)

To determine

The value of f(1).

Expert Solution

Answer to Problem 1E

The value of f(1) is 3.

Explanation of Solution

Given:

Plot the points in the given graph as shown below in Figure 1.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.1, Problem 1E

Calculation:

In Figure.1, x-axis represents the values of x, and y-axis represents the values of f(x).

From Figure 1, it is noticeable that the point (1, 3) is plotted.

Therefore, the value of f(1)=3.

(b)

To determine

The value of f(1).

Expert Solution

Answer to Problem 1E

The value of f(1) is approximately −0.2.

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 f(1)0.2.

(c)

To determine

The value of x if f(x)=1.

Expert Solution

Answer to Problem 1E

If f(x)=1, then the values of x are 0 and 3.

Explanation of Solution

From Figure 1, it is it is noticeable that the points (0, 1) and (3, 1) are plotted.

Therefore, when f(x)=1 the values of x=0,3.

(d)

To determine

The value of x if f(x)=1.

Expert Solution

Answer to Problem 1E

If f(x)=1, then the values of x is approximately −0.8.

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 f(x)=1 the value of x0.8.

(e)

To determine

The domain and range of f.

Expert Solution

Answer to Problem 1E

The domain of f is [2,4] and range of f is [1,3].

Explanation of Solution

Since, the domain of a function is the set of all x values of the graph, the domain is [2,4]. In the interval notation, it can be written as 2x4.

Since, the range of a function is the set of all y values of the graph, the range of the function is [1,3]. In the interval notation, it can be written as −1 ≤ y ≤ 3.

(f)

To determine

The increasing interval of f.

Expert Solution

Answer to Problem 1E

The increasing interval of f is [2,1].

Explanation of Solution

From Figure 1, it is noticeable that the curve is increasing between x=2 and x=1.

Therefore, the increasing interval of f is [2,1].

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