# Thread: Domain & Range Question

1. ## Domain & Range Question

What is the domain & range of this function ?
f (x) = 2 + √x-4

I know that the number under the square root can't be zero or negative.

Thus far I think that:

the domain is R=> 4
the range ? not sure how to calculate

2. Originally Posted by kbgemini16
What is the domain & range of this function ?
f (x) = 2 + √x-4

I know that the number under the square root can't be zero or negative.

Thus far I think that:

the domain is R=> 4
the range ? not sure how to calculate
You have the domain correct.

The range is not as difficult as you may think. What is the minimum value of your function? The radical cannot be less than zero, so the function is at least two. The sky is the limit as far as a maximum is concerned.

3. Originally Posted by colby2152
You have the domain correct.

The range is not as difficult as you may think. What is the minimum value of your function? The radical cannot be less than zero, so the function is at least two. The sky is the limit as far as a maximum is concerned.
ok, so could the range be (5,)

4. Originally Posted by kbgemini16
ok, so could the range be (5,)
No, the range's minimum would be the minimum of the function which is two.

5. Originally Posted by colby2152
No, the range's minimum would be the minimum of the function which is two.
I'm getting confused...

Are you saying the min is 2 because it's 2 + the radical ?

6. Originally Posted by kbgemini16
I'm getting confused...

Are you saying the min is 2 because it's 2 + the radical ?
Yes because the minimum value of the radical is zero. It cannot be negative, but it can be zero (at x = 4), so the minimum of the function is two, and that is the bottom of the range.

7. Originally Posted by colby2152
Yes because the minimum value of the radical is zero. It cannot be negative, but it can be zero (at x = 4), so the minimum of the function is two, and that is the bottom of the range.
I got it now !!!

Thanks so much ...