# How do you find domain and range for #y=sqrt((4 - x²))#?

Refer to explanation

We have that because it's a square root.

The scope is

By signing up, you agree to our Terms of Service and Privacy Policy

To find the domain of the function ( y = \sqrt{4 - x^2} ), we need to determine the values of ( x ) for which the expression under the square root is non-negative. Since the square root of a negative number is not real, ( 4 - x^2 ) must be greater than or equal to zero:

[ 4 - x^2 \geq 0 ]

Solving this inequality:

[ 4 \geq x^2 ]

[ -4 \leq x^2 ]

[ -2 \leq x \leq 2 ]

So, the domain of the function is ( -2 \leq x \leq 2 ).

To find the range, notice that the square root of any non-negative number is always non-negative. Therefore, the range of the function ( y = \sqrt{4 - x^2} ) is all non-negative real numbers, or ( y \geq 0 ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Mattie must pay a $15 co-pay for each of her visits to a chiropractor The company pays 60% of the cost of the visit. After her accident, she made 12 visits to the chiropractor, each costing $305. How much, in total did Mattie pay for her visit?
- How do you find the domain of #f(x) = (3x^2)/(x^2-49)#?
- What is the domain of #g(t)=root4(t+4)#?
- There are 64 in a soccer tournament. Each team plays until it loses one game. There are no ties. How many games are played? You may want to draw a diagram to look for a pattern.
- How do you place the inclusion symbols to make the statement 27+5*8-6=37 true?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7