Which of these statements accurately represents the domain and range of the equation  y=x+4−−−−−√−3
 ?

	
The domain of the equation is  " x is greater than 4" and the range is " y is less than -3".


Domain:  x>4

Range:  y<−3


	
The domain of the equation is " x is greater than or equal to -4" and the range is " y is less than or equal to -3".


Domain:  x≥−4

Range:  y≤−3


	
 The domain of the equation is  " x is greater than or equal to -4" and the range is " y is greater than or equal to -3". 

 


Domain:  x≥−4

Range:  y≥−3


	
The domain of the equation is " x is less than -4" and the range is " y is greater than -3".


Domain:  x<−4

Range:  y>−3

Let's analyze the equation \( y = \sqrt{x + 4} - 3 \) to determine its domain and range.

### Domain:
- The square root function \( \sqrt{x+4} \) is defined only when the expression inside the square root is non-negative. Therefore, \( x + 4 \geq 0 \), which simplifies to \( x \geq -4 \).
- So, the **domain** is \( x \geq -4 \).

### Range:
- When \( x = -4 \), the square root part \( \sqrt{x + 4} \) becomes \( \sqrt{0} = 0 \), and the equation becomes \( y = 0 - 3 = -3 \).
- As \( x \) increases, \( \sqrt{x + 4} \) becomes positive, making \( y = \sqrt{x + 4} - 3 \) larger than \(-3\).
- Therefore, the smallest value of \( y \) is \(-3\), and as \( x \) increases, \( y \) increases without bound.
- So, the **range** is \( y \geq -3 \).

### Conclusion:
The correct answer is:

**The domain of the equation is " x is greater than or equal to -4" and the range is " y is greater than or equal to -3".**

This matches the third option:

**Domain: \( x \geq -4 \)**  
**Range: \( y \geq -3 \)**

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Would you like more details or further explanation?

Here are 5 related questions:
1. How do you find the domain of a function involving square roots?
2. Can the range of a square root function ever include negative values?
3. How does adding or subtracting a constant outside the square root affect the range?
4. What would happen to the domain and range if the function were \( y = -\sqrt{x + 4} - 3 \)?
5. How do transformations like shifting and reflecting impact the domain and range of functions?

**Tip**: For functions involving square roots, always check the inside of the root for non-negative values to determine the domain!

Which of these statements accurately represents the domain and range of the equation y = sqrt(x+4) - 3?

Understand how to determine the domain and range of the equation y = sqrt(x+4) - 3. Learn how the square root function behaves, the restrictions on the domain, and how it impacts the range of the function. This problem is suitable for students in Grades 9-11.

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