### All Precalculus Resources

## Example Questions

### Example Question #7 : Find A Point Of Discontinuity

Find a point of discontinuity for the following function:

**Possible Answers:**

There are no points of discontinuity for this function.

**Correct answer:**

Start by factoring the numerator and denominator of the function.

A point of discontinuity occurs when a number is both a zero of the numerator and denominator.

Since is a zero for both the numerator and denominator, there is a point of discontinuity there. Since the final function is , and are points of discontinuity.

### Example Question #8 : Find A Point Of Discontinuity

Find a point of discontinuity in the following function:

**Possible Answers:**

There is no point of discontinuity for this function.

**Correct answer:**

Start by factoring the numerator and denominator of the function.

A point of discontinuity occurs when a number is both a zero of the numerator and denominator.

Since is a zero for both the numerator and denominator, there is a point of discontinuity there. To find the value, plug in into the final simplified equation.

is the point of discontinuity.

### Example Question #9 : Find A Point Of Discontinuity

Find the point of discontinuity for the following function:

**Possible Answers:**

There is no point of discontinuity.

**Correct answer:**

Start by factoring the numerator and denominator of the function.

A point of discontinuity occurs when a number is both a zero of the numerator and denominator.

Since is a zero for both the numerator and denominator, there is a point of discontinuity there. To find the value, plug in into the final simplified equation.

is the point of discontinuity.

### Example Question #10 : Find A Point Of Discontinuity

Find the point of discontinuity for the following function:

**Possible Answers:**

There is no point of discontinuity for this function.

**Correct answer:**

Start by factoring the numerator and denominator of the function.

A point of discontinuity occurs when a number is both a zero of the numerator and denominator.

Since is a zero for both the numerator and denominator, there is a point of discontinuity there. To find the value, plug in into the final simplified equation.

is the point of discontinuity.

### Example Question #11 : Find A Point Of Discontinuity

Find the point of discontinuity for the following function:

**Possible Answers:**

There is no point of discontinuity for this function.

**Correct answer:**

Start by factoring the numerator and denominator of the function.

A point of discontinuity occurs when a number is both a zero of the numerator and denominator.

is the point of discontinuity.

### Example Question #12 : Find A Point Of Discontinuity

Find the point of discontinuity for the following function:

**Possible Answers:**

There is no point of discontinuity for this function.

**Correct answer:**

Start by factoring the numerator and denominator of the function.

A point of discontinuity occurs when a number is both a zero of the numerator and denominator.

is the point of discontinuity.

### Example Question #13 : Find A Point Of Discontinuity

Find the point of discontinuity for the following function:

**Possible Answers:**

There is no point of discontinuity for this function.

**Correct answer:**

Start by factoring the numerator and denominator of the function.

A point of discontinuity occurs when a number is both a zero of the numerator and denominator.

is the point of discontinuity.

### Example Question #14 : Find A Point Of Discontinuity

Find the point of discontinuity for the following function:

**Possible Answers:**

There is no point of discontinuity for this function.

**Correct answer:**

Start by factoring the numerator and denominator of the function.

A point of discontinuity occurs when a number is both a zero of the numerator and denominator.

is the point of discontinuity.

### Example Question #15 : Find A Point Of Discontinuity

Find the point of discontinuity for the following function:

**Possible Answers:**

There is no discontinuity for this function.

**Correct answer:**

Start by factoring the numerator and denominator of the function.

A point of discontinuity occurs when a number is both a zero of the numerator and denominator.

is the point of discontinuity.

### Example Question #16 : Find A Point Of Discontinuity

Given the function, , where and what is the type of discontinuity, if any?

**Possible Answers:**

**Correct answer:**

Before we simplify, set the denominator equal to zero to determine where is invalid. The value of the denominator cannot equal to zero.

The value at is invalid in the domain.

Pull out a greatest common factor for the numerator and the denominator and simplify.

Since the terms can be cancelled, there will not be any vertical asymptotes. Even though the rational function simplifies to , there will be instead a hole at on the graph.

The answer is:

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