How to graph an exponential function

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Geometry › How to graph an exponential function

Questions 1 - 10
1

Define a function as follows:

Give the vertical aysmptote of the graph of .

The graph of does not have a vertical asymptote.

Explanation

Since any number, positive or negative, can appear as an exponent, the domain of the function is the set of all real numbers; in other words, is defined for all real values of . It is therefore impossible for the graph to have a vertical asymptote.

2

Define a function as follows:

Give the horizontal aysmptote of the graph of .

Explanation

The horizontal asymptote of an exponential function can be found by noting that a positive number raised to any power must be positive. Therefore, and for all real values of . The graph will never crosst the line of the equatin , so this is the horizontal asymptote.

3

Evaluate .

The system has no solution.

Explanation

Rewrite the system as

and substitute and for and , respectively, to form the system

Add both sides:

.

Now backsolve:

Now substitute back:

and

4

Give the -intercept of the graph of the function

Round to the nearest tenth, if applicable.

The graph has no -interceptx

Explanation

The -intercept is , where :

The -intercept is .

5

An important part of graphing an exponential function is to find its -intercept and concavity.

Find the -intercept for

and determine if the graph is concave up or concave down.

Explanation

.

6

Give the -intercept of the graph of the function

Round to the nearest hundredth, if applicable.

The graph has no -intercept

Explanation

The -intercept is :

is the -intercept.

7

Define a function as follows:

Give the -intercept of the graph of .

Explanation

The -coordinate ofthe -intercept of the graph of is 0, and its -coordinate is :

The -intercept is the point .

8

Give the domain of the function .

The set of all real numbers

Explanation

Let . This function is defined for any real number , so the domain of is the set of all real numbers. In terms of ,

Since is defined for all real , so is ; it follows that is as well. The correct domain is the set of all real numbers.

9

Give the -intercept(s) of the graph of the equation

The graph has no -intercept.

Explanation

Set and solve for :

10

Define a function as follows:

Give the -intercept of the graph of .

Explanation

Since the -intercept is the point at which the graph of intersects the -axis, the -coordinate is 0, and the -coordinate is :

,

The -intercept is the point .

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