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, Problem 1RE

(a)

To determine

To estimate: The value of f(2).

Expert Solution

Answer to Problem 1RE

Solution:

The value of f(2) is approximately 2.7.

Explanation of Solution

Let y=f(x) be the function.

From the given graph, it is noticed that when the curve approaches x=2, the corresponding y-axis value is 2.7.

That is, f(2)2.7.

(b)

To determine

To estimate: The value of x when f(x)=3.

Expert Solution

Answer to Problem 1RE

Solution:

The values of x are approximately 2.3 and 5.6.

Explanation of Solution

Let y=f(x) be the function.

From the given graph, it is noticed that when the curve approaches y=3, the corresponding values of x are approximately 2.3 and 5.6.

That is, x2.3 and 5.6.

(c)

To determine

To state: The domain of f.

Expert Solution

Explanation of Solution

The set of all x values of f are called the domain of the graph f.

From the given graph, it is noticed that the values of x – axis are from −6 to 6.

Thus, the domain of the graph is [6,6].

(d)

To determine

To state: The range of f.

Expert Solution

Explanation of Solution

The set of all y values of f are called range of the graph f.

From the given graph, it is noticed that the values of y – axis are from −4 to 4.

Thus, the range of the graph is [4,4].

(e)

To determine

To find: The interval on which f is increasing.

Expert Solution

Explanation of Solution

From the given graph, it is noticed that the curve is increasing between −4 to 4.

Therefore, the function is increasing on the interval [4,4].

(f)

To determine

To check: Whether the function is one-to-one and explain the reason.

Expert Solution

Answer to Problem 1RE

Solution:

The function f is not one-to-one.

Explanation of Solution

In order to find whether the function f is one-to-one or not, use the horizontal line test.

From the given graph, it is observed that for x=2.3 and 5.6 the corresponding y values are the same.

From the above information, it is clear that the horizontal line intersect the curve more than once.

Therefore, the horizontal line test fails.

So, f is not one-to-one.

(g)

To determine

To check: Whether the function is even, odd or neither even nor odd.

Expert Solution

Answer to Problem 1RE

Solution:

The function is odd.

Explanation of Solution

The function is even if f(x)=f(x), the function is odd if f(x)=f(x).

Notice that, when x=4, f(4)=4.

When x=4, f(4)=4.

Thus, f(4)=f(4).

Therefore, the function is odd.

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