What Is The Range Of The Function $y = \sqrt{x + 5}$?A. $y \geq -5$ B. $y \geq 0$ C. $y \geq \sqrt{5}$ D. $y \geq 5$

Introduction

When dealing with functions, understanding the range is crucial in determining the possible output values. The range of a function is the set of all possible output values it can produce for the given input values. In this article, we will explore the range of the function $y = \sqrt{x + 5}$ and determine the correct answer among the given options.

Understanding the Function

The given function is $y = \sqrt{x + 5}$. This is a square root function, which means that the output value $y$ will always be non-negative. The square root function is defined only for non-negative values, and any negative value under the square root sign will result in an imaginary number.

Domain of the Function

Before we can determine the range, we need to understand the domain of the function. The domain of a function is the set of all possible input values. In this case, the function is defined for all real numbers $x$ such that $x + 5 \geq 0$. This means that $x \geq -5$, and the domain of the function is $x \geq -5$.

Range of the Function

Now that we have understood the domain of the function, we can determine the range. Since the function is a square root function, the output value $y$ will always be non-negative. The minimum value of $y$ will occur when $x = -5$, which gives us $y = \sqrt{-5 + 5} = \sqrt{0} = 0$. As $x$ increases, $y$ will also increase, but it will never be negative.

Analyzing the Options

Now that we have determined the range of the function, let's analyze the given options:

A. $y \geq -5$ B. $y \geq 0$ C. $y \geq \sqrt{5}$ D. $y \geq 5$

Conclusion

Based on our analysis, we can conclude that the correct answer is:

B. $y \geq 0$

This is because the range of the function $y = \sqrt{x + 5}$ is all non-negative values, starting from 0.

Final Thoughts

In conclusion, understanding the range of a function is crucial in determining the possible output values. The range of the function $y = \sqrt{x + 5}$ is all non-negative values, starting from 0. This is because the function is a square root function, and the output value $y$ will always be non-negative. We hope this article has provided valuable insights into the range of the function and has helped you understand the concept better.

Frequently Asked Questions

• What is the range of the function $y = \sqrt{x + 5}$?
• Why is the range of the function $y = \sqrt{x + 5}$ all non-negative values?
• What is the minimum value of $y$ in the function $y = \sqrt{x + 5}$?

Answers

• The range of the function $y = \sqrt{x + 5}$ is all non-negative values, starting from 0.
• The range of the function $y = \sqrt{x + 5}$ is all non-negative values because the function is a square root function, and the output value $y$ will always be non-negative.
• The minimum value of $y$ in the function $y = \sqrt{x + 5}$ is 0, which occurs when $x = -5$.
  

Introduction

In our previous article, we explored the range of the function $y = \sqrt{x + 5}$ and determined that the correct answer is $y \geq 0$. However, we received many questions from readers who were still unsure about the concept. In this article, we will address some of the frequently asked questions and provide a deeper understanding of the range of the function.

Q&A

Q1: What is the range of the function $y = \sqrt{x + 5}$?

A1: The range of the function $y = \sqrt{x + 5}$ is all non-negative values, starting from 0. This is because the function is a square root function, and the output value $y$ will always be non-negative.

Q2: Why is the range of the function $y = \sqrt{x + 5}$ all non-negative values?

A2: The range of the function $y = \sqrt{x + 5}$ is all non-negative values because the function is a square root function, and the output value $y$ will always be non-negative. This is due to the fact that the square root of a negative number is an imaginary number, and the function is defined only for non-negative values.

Q3: What is the minimum value of $y$ in the function $y = \sqrt{x + 5}$?

A3: The minimum value of $y$ in the function $y = \sqrt{x + 5}$ is 0, which occurs when $x = -5$. This is because the square root of 0 is 0, and the function is defined only for non-negative values.

Q4: Can the function $y = \sqrt{x + 5}$ produce negative values?

A4: No, the function $y = \sqrt{x + 5}$ cannot produce negative values. This is because the function is a square root function, and the output value $y$ will always be non-negative.

Q5: What happens if $x$ is a negative number?

A5: If $x$ is a negative number, the function $y = \sqrt{x + 5}$ will still produce a non-negative value. This is because the square root of a negative number is an imaginary number, and the function is defined only for non-negative values.

Q6: Can the function $y = \sqrt{x + 5}$ produce zero?

A6: Yes, the function $y = \sqrt{x + 5}$ can produce zero. This occurs when $x = -5$, and the output value $y$ is 0.

Q7: What is the domain of the function $y = \sqrt{x + 5}$?

A7: The domain of the function $y = \sqrt{x + 5}$ is all real numbers $x$ such that $x \geq -5$. This is because the function is defined only for non-negative values.

Q8: Can the function $y = \sqrt{x + 5}$ be defined for negative values of $x$?

A8: No, the function $y = \sqrt{x + 5}$ cannot be defined for negative values of $x$. This is because the function is defined only for non-negative values.

Conclusion

In conclusion, the range of the function $y = \sqrt{x + 5}$ is all non-negative values, starting from 0. This is because the function is a square root function, and the output value $y$ will always be non-negative. We hope this article has provided valuable insights into the range of the function and has helped you understand the concept better.

Frequently Asked Questions

• What is the range of the function $y = \sqrt{x + 5}$?
• Why is the range of the function $y = \sqrt{x + 5}$ all non-negative values?
• What is the minimum value of $y$ in the function $y = \sqrt{x + 5}$?
• Can the function $y = \sqrt{x + 5}$ produce negative values?
• What happens if $x$ is a negative number?
• Can the function $y = \sqrt{x + 5}$ produce zero?
• What is the domain of the function $y = \sqrt{x + 5}$?
• Can the function $y = \sqrt{x + 5}$ be defined for negative values of $x$?

Answers

• The range of the function $y = \sqrt{x + 5}$ is all non-negative values, starting from 0.
• The range of the function $y = \sqrt{x + 5}$ is all non-negative values because the function is a square root function, and the output value $y$ will always be non-negative.
• The minimum value of $y$ in the function $y = \sqrt{x + 5}$ is 0, which occurs when $x = -5$.
• No, the function $y = \sqrt{x + 5}$ cannot produce negative values.
• If $x$ is a negative number, the function $y = \sqrt{x + 5}$ will still produce a non-negative value.
• Yes, the function $y = \sqrt{x + 5}$ can produce zero.
• The domain of the function $y = \sqrt{x + 5}$ is all real numbers $x$ such that $x \geq -5$.
• No, the function $y = \sqrt{x + 5}$ cannot be defined for negative values of $x$.