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. In this case, we are given the function $y = \sqrt{x+5}$, and we need to find its range. The range of a function is the set of all possible output values it can produce for the given input values. In other words, it is the set of all possible y-values that the function can take.

Understanding the Function

The given function is $y = \sqrt{x+5}$. This is a square root function, which means that the output value (y) is the square root of the input value (x+5). The square root function is defined only for non-negative values, which means that the input value (x+5) must be greater than or equal to 0.

Finding the Range

To find the range of the function, we need to determine the possible output values (y-values) that the function can produce. Since the input value (x+5) must be greater than or equal to 0, we can set up the inequality $x+5 \geq 0$. Solving this inequality, we get $x \geq -5$.

Analyzing the Square Root Function

Now that we have the inequality $x \geq -5$, we can analyze the square root function. The square root function is defined only for non-negative values, which means that the output value (y) must be greater than or equal to 0. Therefore, we can set up the inequality $y \geq 0$.

Combining the Inequalities

We have two inequalities: $x \geq -5$ and $y \geq 0$. These inequalities represent the possible input values (x-values) and output values (y-values) of the function. Since the function is defined only for non-negative values, the output value (y) must be greater than or equal to 0.

Conclusion

Based on the analysis, we can conclude that the range of the function $y = \sqrt{x+5}$ is $y \geq 0$. This means that the function can produce any output value greater than or equal to 0.

Comparison with Options

Let's compare our conclusion with the given options:

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

Our conclusion matches option B, which states that $y \geq 0$. Therefore, the correct answer is option B.

Final Answer

The final answer is option B, which states that the range of the function $y = \sqrt{x+5}$ is $y \geq 0$.

Introduction

In our previous article, we discussed the range of the function $y = \sqrt{x+5}$. We concluded that the range of the function is $y \geq 0$. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information.

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 $y \geq 0$. This means that the function can produce any output value greater than or equal to 0.

Q2: Why is the range of the function $y = \sqrt{x+5}$ $y \geq 0$?

A2: The range of the function $y = \sqrt{x+5}$ is $y \geq 0$ because the square root function is defined only for non-negative values. Since the input value (x+5) must be greater than or equal to 0, the output value (y) must also be greater than or equal to 0.

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

A3: The minimum value of the function $y = \sqrt{x+5}$ is 0. This is because the function can produce any output value greater than or equal to 0.

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 square root function is defined only for non-negative values.

Q5: What is the maximum value of the function $y = \sqrt{x+5}$?

A5: The maximum value of the function $y = \sqrt{x+5}$ is not defined. This is because the function can produce any output value greater than or equal to 0, and there is no upper bound.

Q6: How does the function $y = \sqrt{x+5}$ compare to the function $y = x^2$?

A6: The function $y = \sqrt{x+5}$ is different from the function $y = x^2$. The function $y = \sqrt{x+5}$ is defined only for non-negative values, while the function $y = x^2$ is defined for all real values.

Q7: Can the function $y = \sqrt{x+5}$ be used to model real-world phenomena?

A7: Yes, the function $y = \sqrt{x+5}$ can be used to model real-world phenomena. For example, it can be used to model the growth of a population or the spread of a disease.

Q8: How does the function $y = \sqrt{x+5}$ relate to the concept of domain and range?

A8: The function $y = \sqrt{x+5}$ is related to the concept of domain and range. The domain of the function is all real values greater than or equal to -5, and the range of the function is all real values greater than or equal to 0.

Conclusion

In this Q&A article, we provided answers to common questions about the range of the function $y = \sqrt{x+5}$. We hope that this article has helped to clarify any doubts and provide additional information.

Final Answer

The final answer is that the range of the function $y = \sqrt{x+5}$ is $y \geq 0$.