# Homework Help: Finding Domain and Range of Functions

1. Sep 2, 2009

### MorganJ

Find the domain and range of y=sin^2x

I have a hard type computing this into my graphing calculator. Can someone help in the steps to find the domain?

2. Sep 2, 2009

### rock.freak667

y=sin2x=(sinx)2.

since it is squared it is never negative. The domain should be easy to find, given your knowledge of y=sinx

3. Sep 2, 2009

### MorganJ

So the domain would be 0 less than or equal to positive infinity? and the range would be the same?

4. Sep 2, 2009

### rock.freak667

What is the domain of sin(x)? The range is the values of 'y' that the graph lies between.

You know that -1≤ sinx ≤ 1, so where would sin2x lie between?

5. Sep 2, 2009

### MorganJ

the domain of sin (x) is -∞ < x < ∞ and would sin²x lie between -2 ≤ x ≤ 2...sorry i am bit confused.

6. Sep 2, 2009

### rock.freak667

Right, sin2x has the same domain as sin(x)

and would sin²x lie between -2 ≤ x ≤ 2...sorry i am bit confused.[/QUOTE]

if y=sin2x, what is it's maximum and minimum value?

7. Sep 2, 2009

### MorganJ

Wouldn't its maximum value be 1 and the minimum value be -1?

8. Sep 2, 2009

### rock.freak667

yes

remember, sin2x = (sinx)2 so it is a perfect square, meaning sin2x ≥ 0 . So what's the minimum value going to be?

9. Sep 2, 2009

### MorganJ

So...would it be 1 as well?

10. Sep 2, 2009

### rock.freak667

no

in y=x2, what is the lowest value of y which gives a real value for x?

11. Sep 2, 2009

### MorganJ

I have no clue, honestly. I am graphing it on my calculator. Would it be zero? I do not think the minimum value is a negative number.

12. Sep 2, 2009

### rock.freak667

yes it would be zero.

13. Sep 2, 2009

### MorganJ

Okay so the domain would be -∞ < x < ∞ and the range is 0 ≤ y ≤ 1 ?

14. Sep 2, 2009

### rock.freak667

That should be correct. You could write $x \epsilon \Re$ as well I believe.

15. Sep 2, 2009

### MorganJ

Okay. Thank you so much for helping, rock.freak667. I really appreciate it :-)