Finding Domain and Range of Functions

In summary, the domain and range for y=sin^2x is 0 less than or equal to positive infinity and -∞ < x < ∞.
  • #1
MorganJ
32
0
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?
 
Physics news on Phys.org
  • #2
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
So the domain would be 0 less than or equal to positive infinity? and the range would be the same?
 
  • #4
MorganJ said:
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?
 
  • #5
the domain of sin (x) is -∞ < x < ∞ and would sin²x lie between -2 ≤ x ≤ 2...sorry i am bit confused.
 
  • #6
MorganJ said:
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?
 
  • #7
Wouldn't its maximum value be 1 and the minimum value be -1?
 
  • #8
MorganJ said:
Wouldn't its maximum value be 1

yes

MorganJ said:
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?
 
  • #9
So...would it be 1 as well?
 
  • #10
MorganJ said:
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?
 
  • #11
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
MorganJ said:
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.
 
  • #13
Okay so the domain would be -∞ < x < ∞ and the range is 0 ≤ y ≤ 1 ?
 
  • #14
MorganJ said:
Okay so the domain would be -∞ < x < ∞ and the range is 0 ≤ y ≤ 1 ?

That should be correct. You could write [itex] x \epsilon \Re[/itex] as well I believe.
 
  • #15
Okay. Thank you so much for helping, rock.freak667. I really appreciate it :-)
 

What is the definition of a function?

A function is a mathematical relationship between an input value (usually denoted as x) and an output value (usually denoted as y) where each input value has only one corresponding output value.

How do you find the domain of a function?

The domain of a function is the set of all possible input values for which the function is defined. To find the domain, you must look for any restrictions on the independent variable (x) such as division by zero or taking the square root of a negative number. The domain will be all real numbers except for these restricted values.

How do you find the range of a function?

The range of a function is the set of all possible output values for the corresponding input values in the domain. To find the range, you must evaluate the function for all values in the domain and determine the set of resulting output values.

What is the difference between the domain and range of a function?

The domain and range of a function are opposite concepts. The domain is the set of all possible input values, while the range is the set of all possible output values. In other words, the domain is the independent variable and the range is the dependent variable.

Why is it important to find the domain and range of a function?

Knowing the domain and range of a function allows us to understand the behavior of the function and determine the set of values for which the function is defined. This information is essential in solving equations, graphing functions, and making predictions based on the function's behavior.

Similar threads

  • Calculus and Beyond Homework Help
Replies
4
Views
887
  • Calculus and Beyond Homework Help
Replies
9
Views
961
  • Calculus and Beyond Homework Help
Replies
12
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
805
  • Precalculus Mathematics Homework Help
Replies
15
Views
524
  • Precalculus Mathematics Homework Help
Replies
11
Views
318
  • Precalculus Mathematics Homework Help
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
3
Views
508
  • Precalculus Mathematics Homework Help
Replies
23
Views
470
Back
Top