## Emily778 Group Title given no other restrictions what are the domain and range of the following function f(x)=x^2-2x+2 8 months ago 8 months ago

1. Emily778

2. zzr0ck3r

it's there any r reason that you can't plug in all numbers?

3. Emily778

I dunno how. jeez

4. agent0smith

For the domain - are there any x-values that you can NOT plug into this function? If you can plug in any x-value in, the domain is all real numbers. For example - in a function like

5. agent0smith

For example - in a function like y = sqrt x, you can't take the square root of a negative number, so the domain is x>0. For a function like y = x^3, you can plug in any x value, so domain is all real numbers.

6. Emily778

so the answer is all real numbers?

7. agent0smith

Well, are there any numbers you can NOT plug into x^2-2x+2 ? And don't worry if you're confused at first. A lot of my honours precalc students are baffled by finding domain of this... when it's so incredibly easy.

8. Emily778

So is it "D={x|x>=2} R= all real numbers"?

9. agent0smith

Wrong way around. Domain is all real numbers.

10. agent0smith

And you have to find the range, by first finding the vertex of the function.

11. Emily778

D and R are all real numbers?

12. agent0smith

Domain is all real. Range is not. Find the minimum value of the function, by finding the vertex. The x-value of the vertex is given by x = -b/(2a). Once you have x, plug that into the function to find y.