Understanding Domain of Functions

The video tutorial explains how to determine if specific x values are in the domain of given functions f(x), g(x), and h(x). It starts with a review of the concept of domain, emphasizing that a value is in the domain if the function provides a legitimate output for it. The tutorial then evaluates different x values for each function, demonstrating the process of checking if they result in defined outputs. The video covers examples where division by zero and square roots of negative numbers lead to undefined states, thus excluding those x values from the domain.

What does it mean for an x-value to be in the domain of a function?

• The x-value is positive.

• The x-value is negative.

• The function has a legitimate output for that x-value.

• The function is undefined for that x-value.

For the function f(x), is x = -5 in the domain?

• No, because the output is positive.

• No, because the output is undefined.

• Yes, because the output is zero.

• Yes, because the output is negative.

What happens when you evaluate f(x) at x = 3?

• The output is a negative number.

• The output is zero.

• The output is undefined due to division by zero.

• The output is a positive number.

Which of the following x-values is not in the domain of f(x)?

• x = 2

• x = 3

• x = 0

• x = -5

For the function g(x), is x = -3 in the domain?

• Yes, because the output is zero.

• No, because the output is a complex number.

• No, because the output is undefined.

• Yes, because the output is a real number.

What is the result of evaluating g(x) at x = 0?

• The output is zero.

• The output is a negative number.

• The output is a positive number.

• The output is undefined.

For the function g(x), is x = 2 in the domain?

• Yes, because the output is a real number.

• No, because the output is undefined.

• Yes, because the output is zero.

• No, because the output is a complex number.

What is the result of evaluating h(x) at x = -1?

• The output is a negative number.

• The output is a positive number.

• The output is undefined.

• The output is zero.

For the function h(x), is x = 5 in the domain?

• No, because the output is undefined.

• No, because the output is a negative number.

• Yes, because the output is zero.

• Yes, because the output is a positive number.

What happens when you evaluate h(x) at x = 10?

• The output is a positive number.

• The output is a negative number.

• The output is undefined.

• The output is zero.