What Is The Domain Of The Function $y=\sqrt{x}+4$?A. \[$-\infty \ \textless \ X \ \textless \ \infty\$\]B. \[$-4 \leq X \ \textless \ \infty\$\]C. \[$0 \leq X \ \textless \ \infty\$\]D. \[$4 \leq X \

What is the Domain of the Function $y=\sqrt{x}+4$?

The domain of a function is the set of all possible input values for which the function is defined. In other words, it is the set of all possible values of the variable x that can be plugged into the function without causing any problems or undefined results. In this article, we will explore the domain of the function $y=\sqrt{x}+4$.

Understanding the Square Root Function

The square root function, denoted by $\sqrt{x}$, is a mathematical function that returns the square root of a number. The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16.

However, the square root function is only defined for non-negative numbers. This means that the square root of a negative number is undefined, because there is no real number that can be multiplied by itself to give a negative number.

The Domain of the Square Root Function

Since the square root function is only defined for non-negative numbers, the domain of the square root function is all non-negative real numbers. This can be represented mathematically as:

$$x \geq 0$$

Adding 4 to the Square Root Function

Now, let's consider the function $y=\sqrt{x}+4$. This function is simply the square root function with 4 added to it. Since the square root function is only defined for non-negative numbers, the domain of the function $y=\sqrt{x}+4$ must also be non-negative.

However, the addition of 4 to the square root function does not change the fact that the function is only defined for non-negative numbers. This means that the domain of the function $y=\sqrt{x}+4$ is still all non-negative real numbers.

Finding the Domain of the Function

To find the domain of the function $y=\sqrt{x}+4$, we need to consider the values of x that make the function defined. Since the function is only defined for non-negative numbers, we can set up the following inequality:

$$x \geq 0$$

This inequality represents all non-negative real numbers, which is the domain of the function $y=\sqrt{x}+4$.

Comparing the Options

Now, let's compare the options given in the problem:

A. {-\infty \ \textless \ x \ \textless \ \infty$}$ B. {-4 \leq x \ \textless \ \infty$}$ C. ${0 \leq x \ \textless \ \infty\$} D. ${4 \leq x \ \textless \ \infty\$}

Only option C represents the domain of the function $y=\sqrt{x}+4$, which is all non-negative real numbers.

Conclusion

In conclusion, the domain of the function $y=\sqrt{x}+4$ is all non-negative real numbers. This can be represented mathematically as:

$$x \geq 0$$

The correct answer is option C, ${0 \leq x \ \textless \ \infty\$}.

Final Answer

The final answer is C.
Q&A: Domain of the Function $y=\sqrt{x}+4$

In the previous article, we explored the domain of the function $y=\sqrt{x}+4$. In this article, we will answer some frequently asked questions about the domain of this function.

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

A: The domain of the function $y=\sqrt{x}+4$ is all non-negative real numbers. This can be represented mathematically as:

$$x \geq 0$$

Q: Why is the domain of the function $y=\sqrt{x}+4$ all non-negative real numbers?

A: The domain of the function $y=\sqrt{x}+4$ is all non-negative real numbers because the square root function is only defined for non-negative numbers. When we add 4 to the square root function, the domain remains the same.

Q: What happens if we plug in a negative number into the function $y=\sqrt{x}+4$?

A: If we plug in a negative number into the function $y=\sqrt{x}+4$, the function will be undefined. This is because the square root of a negative number is undefined.

Q: Can we plug in zero into the function $y=\sqrt{x}+4$?

A: Yes, we can plug in zero into the function $y=\sqrt{x}+4$. In fact, zero is a part of the domain of the function.

Q: What is the relationship between the domain of the function $y=\sqrt{x}+4$ and the square root function?

A: The domain of the function $y=\sqrt{x}+4$ is the same as the domain of the square root function. This is because the addition of 4 to the square root function does not change the domain.

Q: Can we find the domain of the function $y=\sqrt{x}+4$ using a graph?

A: Yes, we can find the domain of the function $y=\sqrt{x}+4$ using a graph. The graph of the function will only be defined for non-negative values of x.

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

A: The domain of the function $y=\sqrt{x}+4$ is significant because it tells us the values of x for which the function is defined. This is important in mathematics and real-world applications.

Q: Can we generalize the domain of the function $y=\sqrt{x}+4$ to other functions?

A: Yes, we can generalize the domain of the function $y=\sqrt{x}+4$ to other functions. The domain of a function is the set of all possible input values for which the function is defined.

Conclusion

In conclusion, the domain of the function $y=\sqrt{x}+4$ is all non-negative real numbers. This is because the square root function is only defined for non-negative numbers, and the addition of 4 to the square root function does not change the domain. We hope that this Q&A article has helped to clarify any questions you may have had about the domain of the function $y=\sqrt{x}+4$.

Final Answer

The final answer is C.