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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1, Problem 1RE

(a)

To determine

**To estimate:** The value of

Expert Solution

**Solution:**

The value of

Let

From the given graph, it is noticed that when the curve approaches *y*-axis value is 2.7.

That is,

(b)

To determine

**To estimate:** The value of *x* when

Expert Solution

**Solution:**

The values of *x* are approximately 2.3 and 5.6.

Let

From the given graph, it is noticed that when the curve approaches *x* are approximately 2.3 and 5.6.

That is,

(c)

To determine

**To state:** The domain of *f*.

Expert 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

(d)

To determine

**To state:** The range of *f*.

Expert 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

(e)

To determine

**To find:** The interval on which *f* is increasing.

Expert 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

(f)

To determine

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

Expert Solution

**Solution:**

The function *f* is not one-to-one.

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 *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

**Solution:**

The function is odd.

The function is even if

Notice that, when

When

Thus,

Therefore, the function is odd.