# ACT Math : How to graph an exponential function

## Example Questions

### Example Question #2 : Graph A Polynomial 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 #1 : 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 #1 : 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 #3 : 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 #1 : 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 #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 set the expressions equal, as follows: