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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.5, Problem 5E

(a)

To determine

**To write:** An equation of the exponential function with base

Expert Solution

The equation that defines the exponential function is

An exponential function is a function of the form *a* is a positive constant called its base.

The equation of the exponential function with base

Notice that this function is not defined when

Therefore, the equation of the exponential function with base

(b)

To determine

The domain of the exponential function obtained in part (a).

Expert Solution

The domain of the exponential function

The domain of a function is defined as the set of all possible values of the independent variable of the function for which the function is defined.

Consider the exponential function *x*.

Since the function *x*, its domain will be the set all real values, that is

Therefore, the domain of the exponential function

(c)

To determine

The range of the function

Expert Solution

The range of the function

The range of a function is defined as the set of all possible values of the dependent variable of the function.

Consider the exponential function *y*.

Since *y* is always positive.

So the range of the function is the set of all positive real values.

Therefore, the range of the function

(d)

(i)

To determine

**To sketch:** The graph of the exponential function if

Expert Solution

The graph of the exponential function

From Figure 1, it is observed that the graph is monotonically increasing.

(ii)

To determine

**To sketch:** The graph of the exponential function if

Expert Solution

The graph of the exponential function

From Figure 2, it is observed that the graph is parallel to *x*-axis as the function is a constant.

(iii)

To determine

**To sketch:** The graph of the exponential function if

Expert Solution

The graph of the exponential function

From Figure 3, it is observed that the graph is monotonically decreasing.