Consider The Function $y = \sqrt{x - 5}$.What Are The Domain And Range Of This Function?A. Domain: $x \leq 0$, Range: $y \geq 5$B. Domain: $x \geq 5$, Range: $y \geq 0$C. Domain: $x \leq 5$, Range:

Introduction

When dealing with functions, it's essential to understand the domain and range of a function. The domain of a function is the set of all possible input values for which the function is defined, while the range is the set of all possible output values. In this article, we will explore the domain and range of the function $y = \sqrt{x - 5}$.

What is the Domain of a Function?

The domain of a function is the set of all possible input values for which the function is defined. In other words, it's the set of all possible values of $x$ that can be plugged into the function. For the function $y = \sqrt{x - 5}$, we need to find the values of $x$ for which the expression under the square root is non-negative.

Finding the Domain of the Function

To find the domain of the function $y = \sqrt{x - 5}$, we need to find the values of $x$ for which the expression under the square root is non-negative. This means that $x - 5 \geq 0$. Solving for $x$, we get $x \geq 5$. Therefore, the domain of the function $y = \sqrt{x - 5}$ is $x \geq 5$.

What is the Range of a Function?

The range of a function is the set of all possible output values for which the function is defined. In other words, it's the set of all possible values of $y$ that can be obtained by plugging in different values of $x$. For the function $y = \sqrt{x - 5}$, we need to find the values of $y$ for which the expression under the square root is non-negative.

Finding the Range of the Function

To find the range of the function $y = \sqrt{x - 5}$, we need to find the values of $y$ for which the expression under the square root is non-negative. This means that $y^2 \geq 0$. Since $y^2$ is always non-negative, the range of the function $y = \sqrt{x - 5}$ is $y \geq 0$.

Conclusion

In conclusion, the domain of the function $y = \sqrt{x - 5}$ is $x \geq 5$, and the range of the function is $y \geq 0$. Therefore, the correct answer is:

B. Domain: $x \geq 5$, Range: $y \geq 0$

Example Questions

1. What is the domain of the function $y = \sqrt{x + 2}$?
2. What is the range of the function $y = \sqrt{x - 3}$?
3. What is the domain of the function $y = \sqrt{x - 1}$?
4. What is the range of the function $y = \sqrt{x + 1}$?

Answer Key

1. The domain of the function $y = \sqrt{x + 2}$ is $x \geq -2$.
2. The range of the function $y = \sqrt{x - 3}$ is $y \geq 0$.
3. The domain of the function $y = \sqrt{x - 1}$ is $x \geq 1$.
4. The range of the function $y = \sqrt{x + 1}$ is $y \geq 0$.

Final Thoughts

Q: What is the domain of the function $y = \sqrt{x - 2}$?

A: The domain of the function $y = \sqrt{x - 2}$ is $x \geq 2$. This is because the expression under the square root must be non-negative, so $x - 2 \geq 0$, which gives $x \geq 2$.

Q: What is the range of the function $y = \sqrt{x + 3}$?

A: The range of the function $y = \sqrt{x + 3}$ is $y \geq 0$. This is because the square root of any non-negative number is non-negative, so $y \geq 0$.

Q: What is the domain of the function $y = \sqrt{x - 4}$?

A: The domain of the function $y = \sqrt{x - 4}$ is $x \geq 4$. This is because the expression under the square root must be non-negative, so $x - 4 \geq 0$, which gives $x \geq 4$.

Q: What is the range of the function $y = \sqrt{x - 1}$?

A: The range of the function $y = \sqrt{x - 1}$ is $y \geq 0$. This is because the square root of any non-negative number is non-negative, so $y \geq 0$.

Q: What is the domain of the function $y = \sqrt{x + 1}$?

A: The domain of the function $y = \sqrt{x + 1}$ is $x \geq -1$. This is because the expression under the square root must be non-negative, so $x + 1 \geq 0$, which gives $x \geq -1$.

Q: What is the range of the function $y = \sqrt{x - 6}$?

A: The range of the function $y = \sqrt{x - 6}$ is $y \geq 0$. This is because the square root of any non-negative number is non-negative, so $y \geq 0$.

Q: What is the domain of the function $y = \sqrt{x - 3}$?

A: The domain of the function $y = \sqrt{x - 3}$ is $x \geq 3$. This is because the expression under the square root must be non-negative, so $x - 3 \geq 0$, which gives $x \geq 3$.

Q: What is the range of the function $y = \sqrt{x + 2}$?

A: The range of the function $y = \sqrt{x + 2}$ is $y \geq 0$. This is because the square root of any non-negative number is non-negative, so $y \geq 0$.

Q: What is the domain of the function $y = \sqrt{x - 9}$?

A: The domain of the function $y = \sqrt{x - 9}$ is $x \geq 9$. This is because the expression under the square root must be non-negative, so $x - 9 \geq 0$, which gives $x \geq 9$.

Q: What is the range of the function $y = \sqrt{x - 5}$?

A: The range of the function $y = \sqrt{x - 5}$ is $y \geq 0$. This is because the square root of any non-negative number is non-negative, so $y \geq 0$.

Conclusion

In this article, we answered a series of questions about the domain and range of a square root function. We found that the domain of a square root function is the set of all values of $x$ for which the expression under the square root is non-negative, and the range is the set of all non-negative values of $y$. We also provided example questions and answers to help reinforce the concepts learned in this article.