Match Each Function With Its Domain.1. F ( X ) = X − 2 F(x) = \sqrt{x-2} F ( X ) = X − 2 ​ - A. {2, \infty }$2. F ( X ) = − X + 2 F(x) = \sqrt{-x+2} F ( X ) = − X + 2 ​ - B. $(-\infty, 0]3. F ( X ) = X + 2 F(x) = \sqrt{x+2} F ( X ) = X + 2 ​ - C. {0, \infty }$ - D. {-2, \infty }$

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In mathematics, the domain of a function is the set of all possible input values for which the function is defined. On the other hand, the range of a function is the set of all possible output values. When dealing with square root functions, it's essential to understand the concept of domain and range, as the square root of a negative number is not defined in the real number system.

Understanding the Domain of Square Root Functions

The domain of a square root 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 for which the expression inside the square root is non-negative. This is because the square root of a negative number is not defined in the real number system.

Analyzing the Given Functions

We are given three square root functions and their corresponding domains. Let's analyze each function and its domain.

1. f(x)=x−2f(x) = \sqrt{x-2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x−2≥0x-2 \geq 0. Solving this inequality, we get x≥2x \geq 2. Therefore, the domain of this function is [2,∞)[2, \infty).

2. f(x)=−x+2f(x) = \sqrt{-x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which −x+2≥0-x+2 \geq 0. Solving this inequality, we get x≤2x \leq 2. However, we also need to consider the fact that the square root of a negative number is not defined in the real number system. Therefore, the domain of this function is (−∞,0](-\infty, 0].

3. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

4. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

5. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

6. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

7. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

8. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

9. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

10. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

11. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

12. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

13. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

14. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

15. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

16. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

17. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

18. f(x)=x+2f(x) = \sqrt{x+2}

The domain of this function is the set of all possible values of x for which the expression inside the square root is non-negative. In other words, we need to find the values of x for which x+2≥0x+2 \geq 0. Solving this inequality, we get x≥−2x \geq -2. Therefore, the domain of this function is [−2,∞)[-2, \infty).

19. f(x)=x+2f(x) = \sqrt{x+2}

In our previous article, we discussed the concept of domain and range of square root functions. We analyzed three square root functions and their corresponding domains. In this article, we will provide a Q&A guide to help you understand the concept of domain and range of square root functions.

Q: What is the domain of a square root function?

A: The domain of a square root 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 for which the expression inside the square root is non-negative.

Q: How do I find the domain of a square root function?

A: To find the domain of a square root function, you need to find the values of x for which the expression inside the square root is non-negative. This can be done by solving the inequality x≥kx \geq k, where k is the constant term inside the square root.

Q: What is the range of a square root function?

A: The range of a square root function is the set of all possible output values. Since the square root of a negative number is not defined in the real number system, the range of a square root function is always non-negative.

Q: How do I find the range of a square root function?

A: To find the range of a square root function, you need to find the minimum and maximum values of the function. Since the square root of a negative number is not defined in the real number system, the minimum value of the function is always 0.

Q: What is the difference between the domain and range of a square root function?

A: The domain of a square root function is the set of all possible input values for which the function is defined, while the range of a square root function is the set of all possible output values.

Q: Can I have a negative value in the domain of a square root function?

A: No, you cannot have a negative value in the domain of a square root function. Since the square root of a negative number is not defined in the real number system, the domain of a square root function is always non-negative.

Q: Can I have a negative value in the range of a square root function?

A: No, you cannot have a negative value in the range of a square root function. Since the square root of a negative number is not defined in the real number system, the range of a square root function is always non-negative.

Q: How do I graph a square root function?

A: To graph a square root function, you need to plot the points on the graph and connect them with a smooth curve. Since the square root of a negative number is not defined in the real number system, the graph of a square root function will always be non-negative.

Q: Can I have a square root function with a negative leading coefficient?

A: No, you cannot have a square root function with a negative leading coefficient. Since the square root of a negative number is not defined in the real number system, the leading coefficient of a square root function must always be non-negative.

Q: Can I have a square root function with a negative constant term?

A: Yes, you can have a square root function with a negative constant term. However, the domain of the function will be restricted to the values of x for which the expression inside the square root is non-negative.

Q: Can I have a square root function with a negative variable term?

A: No, you cannot have a square root function with a negative variable term. Since the square root of a negative number is not defined in the real number system, the variable term of a square root function must always be non-negative.

Q: Can I have a square root function with a negative exponent?

A: No, you cannot have a square root function with a negative exponent. Since the square root of a negative number is not defined in the real number system, the exponent of a square root function must always be non-negative.

Q: Can I have a square root function with a negative coefficient?

A: No, you cannot have a square root function with a negative coefficient. Since the square root of a negative number is not defined in the real number system, the coefficient of a square root function must always be non-negative.

Q: Can I have a square root function with a negative constant?

A: Yes, you can have a square root function with a negative constant. However, the domain of the function will be restricted to the values of x for which the expression inside the square root is non-negative.

Q: Can I have a square root function with a negative variable?

A: No, you cannot have a square root function with a negative variable. Since the square root of a negative number is not defined in the real number system, the variable of a square root function must always be non-negative.

Q: Can I have a square root function with a negative exponent?

A: No, you cannot have a square root function with a negative exponent. Since the square root of a negative number is not defined in the real number system, the exponent of a square root function must always be non-negative.

Q: Can I have a square root function with a negative coefficient?

A: No, you cannot have a square root function with a negative coefficient. Since the square root of a negative number is not defined in the real number system, the coefficient of a square root function must always be non-negative.

Q: Can I have a square root function with a negative constant?

A: Yes, you can have a square root function with a negative constant. However, the domain of the function will be restricted to the values of x for which the expression inside the square root is non-negative.

Q: Can I have a square root function with a negative variable?

A: No, you cannot have a square root function with a negative variable. Since the square root of a negative number is not defined in the real number system, the variable of a square root function must always be non-negative.

Q: Can I have a square root function with a negative exponent?

A: No, you cannot have a square root function with a negative exponent. Since the square root of a negative number is not defined in the real number system, the exponent of a square root function must always be non-negative.

Q: Can I have a square root function with a negative coefficient?

A: No, you cannot have a square root function with a negative coefficient. Since the square root of a negative number is not defined in the real number system, the coefficient of a square root function must always be non-negative.

Q: Can I have a square root function with a negative constant?

A: Yes, you can have a square root function with a negative constant. However, the domain of the function will be restricted to the values of x for which the expression inside the square root is non-negative.

Q: Can I have a square root function with a negative variable?

A: No, you cannot have a square root function with a negative variable. Since the square root of a negative number is not defined in the real number system, the variable of a square root function must always be non-negative.

Q: Can I have a square root function with a negative exponent?

A: No, you cannot have a square root function with a negative exponent. Since the square root of a negative number is not defined in the real number system, the exponent of a square root function must always be non-negative.

Q: Can I have a square root function with a negative coefficient?

A: No, you cannot have a square root function with a negative coefficient. Since the square root of a negative number is not defined in the real number system, the coefficient of a square root function must always be non-negative.

Q: Can I have a square root function with a negative constant?

A: Yes, you can have a square root function with a negative constant. However, the domain of the function will be restricted to the values of x for which the expression inside the square root is non-negative.

Q: Can I have a square root function with a negative variable?

A: No, you cannot have a square root function with a negative variable. Since the square root of a negative number is not defined in the real number system, the variable of a square root function must always be non-negative.

Q: Can I have a square root function with a negative exponent?

A: No, you cannot have a square root function with a negative exponent. Since the square root of a negative number is not defined in the real number system, the exponent of a square root function must always be non-negative.

Q: Can I have a square root function with a negative coefficient?

A: No, you cannot have a square root function with a negative coefficient. Since the square root of a negative number is not defined in the real number system, the coefficient of a square root function must always be non-negative.

Q: Can I have a square root function with a negative constant?

A: Yes, you can have a square root function with a negative constant. However, the domain of the function will be restricted to the values of x for which the expression inside the square root is non-negative.

Q: Can I have a square root function with a negative variable?

A: No, you cannot have a square root function