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.

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.

 Add  on both sides.

 Take the square root of both sides. Remember it can also be negative.

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. However, because there's a fraction inside the radical, we should focus on that first. Remember, the denominator must not be zero. This would make the function undefined. 

 Subtract  on both sides.

 Let's check values greater than this for the radical function. Let's pick .

 This is good as this value is greater than zero. Let's pick a value less than  such as .

 This is not good as this value is less than zero and that's not acceptable in radical conditions. Therefore our answer will be . Remember  is not included. This makes the denominator zero and the whole function becomes undefined.

Because the domain is giving us a wide range of  values, we can easily eliminate the fractional function  as it only isolates a single  value. We can eliminate  as it means I am restricted to  as my domain but I am looking for domain values greater than . This leaves us with the radical functions.

We have to remember the smallest possible value inside the radical is zero. Anything less means we will be dealing with imaginary numbers.

 ,  This means the domain is  which doesn't match our domain so this is wrong. 

 , . This means the domain is  which doesn't match our domain since we want to EXCLUDE  so this is wrong. 

 Since this is fractional expression with a radical in the denominator, we need to remember the bottom can't be zero and just set that denominator to equal .  Square both sides to get .  This actually means  is not acceptable but any values greater than that is good. 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.