Advanced Geometry : How to graph an exponential function

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.

The graph has no -interceptx

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.

The graph has no -intercept

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

The graph of  has no vertical asymptote.

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

The graph has no horizontal asymptote.

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.

The graphs of  and  would not intersect.

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.

The graphs of  and  would not intersect.

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,

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.

Explanation:

.

Example Question #41 : Coordinate Geometry

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

The graph of  has no vertical asymptote.

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 .

The graph of  has no horizontal asymptote.