Finding Domain and Range of Functions

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?

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rock.freak667

Homework Helper
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

MorganJ

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

rock.freak667

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

MorganJ

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

rock.freak667

Homework Helper
the domain of sin (x) is -∞ < x < ∞
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?

MorganJ

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

rock.freak667

Homework Helper
Wouldn't its maximum value be 1
yes

and the minimum value be -1?
remember, sin2x = (sinx)2 so it is a perfect square, meaning sin2x ≥ 0 . So what's the minimum value going to be?

MorganJ

So...would it be 1 as well?

rock.freak667

Homework Helper
So...would it be 1 as well?
no

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

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.

rock.freak667

Homework Helper
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.
yes it would be zero.

MorganJ

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

rock.freak667

Homework Helper
Okay so the domain would be -∞ < x < ∞ and the range is 0 ≤ y ≤ 1 ?
That should be correct. You could write $x \epsilon \Re$ as well I believe.

MorganJ

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

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