### All Advanced Geometry Resources

## 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:**

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:**

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.

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:**

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:**

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:**

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:**

### 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:**

.

### 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.

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:**

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.