Advanced Geometry : How to graph an exponential function

Study concepts, example questions & explanations for Advanced Geometry

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Example Questions

Example Question #1 : How To Graph An Exponential Function

Give the -intercept of the graph of the function

Round to the nearest tenth, if applicable.

Possible Answers:

The graph has no -interceptx

Correct answer:

Explanation:

The -intercept is , where :

The -intercept is .

Example Question #2 : How To Graph An Exponential Function

Give the -intercept of the graph of the function

Round to the nearest hundredth, if applicable.

Possible Answers:

The graph has no -intercept

Correct answer:

Explanation:

The -intercept is :

 is the -intercept.

Example Question #3 : How To Graph An Exponential Function

Give the vertical asymptote of the graph of the function 

Possible Answers:

The graph of  has no vertical asymptote.

Correct answer:

The graph of  has no vertical asymptote.

Explanation:

Since 4 can be raised to the power of any real number, the domain of  is the set of all real numbers. Therefore, there is no vertical asymptote of the graph of .

Example Question #4 : How To Graph An Exponential Function

Give the horizontal asymptote of the graph of the function 

Possible Answers:

The graph has no horizontal asymptote.

Correct answer:

Explanation:

We can rewrite this as follows:

This is a translation of the graph of , which has  as its horizontal asymptote, to the right two units and down three units. Because of the latter translation, the horizontal asymptote is .

Example Question #5 : How To Graph An Exponential Function

If the functions 

were graphed on the same coordinate axes, what would be the -coordinate of their point of intersection?

Round to the nearest tenth, if applicable.

Possible Answers:

The graphs of  and  would not intersect.

Correct answer:

Explanation:

We can rewrite the statements using  for both  and  as follows:

To solve this, we can multiply the first equation by , then add:

      

            

Example Question #6 : How To Graph An Exponential Function

If the functions 

were graphed on the same coordinate axes, what would be the -coordinate of their point of intersection?

Round to the nearest tenth, if applicable.

Possible Answers:

The graphs of  and  would not intersect.

Correct answer:

Explanation:

We can rewrite the statements using  for both  and  as follows:

To solve this, we can set the expressions equal, as follows:

Example Question #11 : How To Graph An Exponential Function

Find the range for,

Possible Answers:

Correct answer:

Explanation:

Example Question #12 : How To Graph An Exponential Function

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.

Possible Answers:

Correct answer:

Explanation:

.

Example Question #41 : Coordinate Geometry

Give the equation of the vertical asymptote of the graph of the equation .

Possible Answers:

The graph of  has no vertical asymptote.

Correct answer:

The graph of  has no vertical asymptote.

Explanation:

Define . In terms of  can be restated as

The graph of  is a transformation of that of . As an exponential function,  has a graph that has no vertical asymptote, as  is defined for all real values of ; it follows that being a transformation of this function,  also has a graph with no vertical asymptote as well.

Example Question #14 : How To Graph An Exponential Function

Give the equation of the horizontal asymptote of the graph of the equation .

Possible Answers:

The graph of  has no horizontal asymptote.

Correct answer:

Explanation:

Define . In terms of  can be restated as

.

The graph of  has as its horizontal asymptote the line of the equation . The graph of  is a transformation of that of  - a right shift of 3 units (  ), a vertical stretch (  ), and a downward shift of 7 units (  ). The right shift and the vertical stretch do not affect the position of the horizontal asymptote, but the downward shift moves the asymptote to the line of the equation . This is the correct response.

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