Domain is finding the acceptable  values that will make the function generate real values.  is an absolute value function therefore any  values will always generate real values. Answer is all real numbers.

Domain is finding the acceptable  values that will make the function generate real values. Because this function is a fractional expression, we need to check the denominator. Remember, the denominator must not be zero. This would make the function undefined. 

 We only need to look at . Since we know it can't equal zero, we set that expression to zero to determine the -value that makes this function undefined.

 Subtract  on both sides.

Domain is finding the acceptable  values that will make the function generate real values. Because we have a radical, we have to remember the smallest possible value inside the radical is zero. Anything less means we will be dealing with imaginary numbers.

 So let's set  to ensure the smallest value inside is zero and makes all possible  values real.

 Subtract  on both sides.

 This means that all values greater than or equal to  will satisfy the equation .

Because the domain is specifying certain numbers not being acceptable in the domain, we can eliminate the radical choice. The cubic equation is also wrong as it's not a fractional function. Let's look at the remaining choices since they are fractional expressions. Our main focus will be setting that denominator to zero as it makes the function undefined.

 Therefore  or . This doesn't satisfy it as we are looking for values of  to also not work. This answer is wrong.

 Therefore , , . This doesn't satisfy it as we are looking for values of  to also not work. Also  is acceptable according to the domain in the question. This answer is wrong.

 Therefore , . Also , . Finally , . This is the correct answer.

Range is the  value generated from a real  value.  is a linear function therefore any  values will always generate real values. Answer is all real numbers.

Range is the  value generated from a real  value. In a quadratic equation, the graph is a parabola with the graph being symmetric. Since the  is positive, we can determine the smallest  value. By determining the vertex of the graph, this will help us with the answer. The vertex of a quadratic equation is  in which  represent the values of a quadratic equation in  form.

 ,  Now let's plug into the vertex equation.

 This is only the  coordinate. We need to plug back into the quadratic equation to get the  value.

, . This means that the lowest range value of that quadratic equation is .

Answer is 

Range is the  value generated from a real  value. Because this function is a fractional expression, we need to check the denominator. Remember, the denominator must not be zero. This would make the function undefined. 

 We only need to look at . Since we know it can't equal zero, we set that expression to zero to determine the -value that makes this function undefined.

 Subtract  on both sides.

 Let's check two different values such as  and . The reason I pick these values is because they approach  from both directions. By doing this, we can check the ranges. 

If , we get a small negative value. When we divide a small negative value, the answer is negative infinity. The same applies when . We will get a small positive value and when we divide a small positive value, we get infinity. Finally, let's check if  is a large negative and large positive number. 

If  we get an extremely small positive number and if , we get an extremely small negative number. It seems like we never reach zero BUT JUST APPROACH IT. Therefore, the range is all real numbers except .

Domain is finding the acceptable  values that will make the function generate real values.  is a linear function therefore any  values will always generate real values. Answer is all real numbers.

Domain is finding the acceptable  values that will make the function generate real values.  is a quadratic function therefore any  values will always generate real values. Answer is all real numbers.

Domain is finding the acceptable  values that will make the function generate real values.  is an absolute value function therefore any  values will always generate real values. Answer is all real numbers.