### All ACT Math Resources

## Example Questions

### Example Question #128 : Advanced Geometry

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 #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:**

The -intercept is :

is the -intercept.

### Example Question #130 : Advanced Geometry

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 #1 : 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 #2 : 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 #3 : 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:

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