### All Algebra II Resources

## Example Questions

### Example Question #1 : Graphing Radical Functions

State the domain of the function:

**Possible Answers:**

**Correct answer:**

Since the expression under the radical cannot be negative,

.

Solve for x:

This is the domain, or possible * *values, for the function.

### Example Question #2 : Graphing Radical Functions

Simplify the radical expression.

**Possible Answers:**

**Correct answer:**

To simplify the radical we need to break the number under the radical sign into its factors.

Since we are able to factor out 9 which is a perfect square, our radical becomes:

### Example Question #3 : Graphing Radical Functions

Simplify the radical expression.

**Possible Answers:**

**Correct answer:**

To simplify the radical we need to factor the number under the radical sign.

Since we can factor out 16 which is a perfect square, the radical becomes:

### Example Question #4 : Graphing Radical Functions

Simplify the radical expression

**Possible Answers:**

**Correct answer:**

To simplify the radical we need to factor the number under the radical sign.

Since we can factor out a 25 which is a perfect square, the radical becomes:

### Example Question #5 : Graphing Radical Functions

Simplify the radical expression

**Possible Answers:**

**Correct answer:**

To simplify the radical we need to first factor the number under the radical sign.

Since we can factor out a 25 and 4 which are perfect squares, our radical becomes:

### Example Question #6 : Graphing Radical Functions

Which of the following choices correctly describes the domain of the graph of the function?

**Possible Answers:**

All real numbers

**Correct answer:**

Because the term inside the radical in the numerator has to be greater than or equal to zero, there is a restriction on our domain; to describe this restriction we solve the inequality for :

Add to both sides, and the resulting inequality is:

or

Next, we consider the denominator, a quadratic; we know that we cannot divide by zero, so we must find x-values that make the denominator equal zero, and exclude them from our domain:

We factor an out of both and :

Finding the zeroes of our expression leaves us with:

Therefore, there are 3 restrictions on the domain of the function: