The absolute value of a number cannot be negative. 

The domain is all the possible values of . To determine the domain, we need to determine what values don't work for this equation. The only value that is not allowed for this equation is 5, since that would make the denominator have a value of , and you can not divide by . Therefore, the domain of this equation is:

 and 

The domain of a rational function is the set of all values of  for which the denominator is not equal to 0, so we set the denominator to 0 and solve for .

This is a quadratic function, so we factor the expression as , replacing the question marks with two numbers whose product is 9 and whose sum is . These numbers are , so

becomes 

,

or .

This means that , or .

Therefore, 3 is the only number excluded from the domain.

The domain of a rational function is the set of all values of  for which the denominator is not equal to 0 (the value of the numerator is irrelevant), so we set the denominator to 0 and solve for  to find the excluded values.

This is a quadratic function, so we factor the expression as , replacing the question marks with two numbers whose product is 8 and whose sum is . These numbers are , so

becomes

So either 

, in which case , 

or , in which case .

Therefore, 2 and 4 are the only numbers excluded from the domain.

In order for the function to be real, the value inside of the square root must be greater than or equal to zero. The domain refers to the possible values of the independent variable (x-value) that allow this to be true.

For this term to be real, must be greater than or equal to zero.

The domain is the set of all potential x-values. In this case, the graph does not extend to the left of  nor to the right of , so the x-values stay between these numbers. We would write this inequality as follows: .

The range is the set of all potential y-values. In this case, the graph does not extend above  or below , so the y-values stay between these numbers. We would write this inequality as follows: .

The domain is the set of all potential x-values. In this case, the graph starts at  and never extends to the left of this point. This means that , inclusive.  The range is the set of all potential y-values. In this case, there are no restrictions on the y-axis, so the range is the set of all real numbers.

Based on the denominator, the only value for which  does not exist is . Therefore, the domain exists for all value except for 3. In interval notation, the domain is 

The range of a function represents all values of  that make the function true. On the other hand, the domain represents all values of  that make the function true.

The parabola  has a range that includes all numbers that are greater than or equal to . This is true because when , .

The range of this parabola is .

Domain looks at x-values and range looks at y-values.

The x-values appear to continue to go on forever, which suggests the answer:

"all real numbers"

The y-values are all number that are equal to nine or less which is

So you answer is:

Domain: All real numbers

Range: