Understanding Functions and Their Domains

This video tutorial covers section 2.1, focusing on functions. It explains how to describe relations, determine if they represent functions, use function notation, find function values, and calculate the difference quotient. The tutorial also discusses finding the domain of functions and performing operations like sum, difference, product, and quotient on functions. Examples are provided to illustrate these concepts, and the importance of the difference quotient in calculus is highlighted.

What is a function in terms of relations?

• A relation where each element of the domain is paired with multiple elements of the range.

• A relation where elements of the range are paired with multiple elements of the domain.

• A relation where each element of the domain is paired with exactly one element of the range.

• A relation where elements of the domain are not paired with any elements of the range.

Which of the following is true about function notation?

• f(x) represents the multiplication of f and x.

• f(x) is used to denote a function and is not a multiplication.

• f(x) is only used for linear functions.

• f(x) is used to denote the range of a function.

What is the difference quotient used for?

• To find the maximum value of a function.

• To determine if a function is linear.

• To calculate the rate of change of a function.

• To find the minimum value of a function.

How do you determine the domain of a function?

• By determining the slope of the function.

• By calculating the maximum value of the function.

• By finding the range of the function.

• By identifying values that make the function undefined.

What is the domain of the function f(x) = x^2 + 5x?

• x ≠ 0

• All real numbers

• x > 0

• x < 0

What is the domain of the function h(t) = √(4 - 3t)?

• t ≤ 4/3

• t ≥ 4/3

• t < 4/3

• t > 4/3

What is the domain of the function g(x) = 3x/(x^2 - 4)?

• x ≠ 0

• x < 0

• x > 0

• x ≠ 2, -2

Which operation on functions requires checking for division by zero?

• Addition

• Subtraction

• Division

• Multiplication

What is the result of adding two functions f(x) and g(x)?

• f(x) * g(x)

• f(x) + g(x)

• f(x) - g(x)

• f(x) / g(x)

If f(x) = 1/(x+2) and g(x) = x/(x-1), what is the domain of f(x) - g(x)?

• x ≠ -2, 0

• x ≠ 0, 1

• x ≠ 1, 2

• x ≠ -2, 1