Understanding Domains of Functions

The video tutorial explains how to determine the domain of different types of functions using interval notation. It covers rational functions, square root functions, and natural log functions. For rational functions, the domain excludes values that make the denominator zero. For square root functions, the domain includes values that make the radicand non-negative. For natural log functions, the domain includes values that make the argument positive. The tutorial provides step-by-step solutions and graphing techniques to visualize the domains.

What is the first step in finding the domain of a rational function?

• Set the function equal to zero

• Set the denominator equal to zero

• Set the numerator equal to zero

• Set the entire expression equal to zero

Why is zero not included in the domain of the function y = 1/x?

• Because zero is a negative number

• Because zero is an even number

• Because division by zero is undefined

• Because zero is a positive number

What is the domain of the function f(x) = 1/(5 - 2x) in interval notation?

• (-∞, 5/2) ∪ (5/2, ∞)

• [5/2, ∞)

• (-∞, 5/2]

• (-∞, ∞)

For a square root function, what must be true about the radicand?

• It must be non-negative

• It must be negative

• It must be positive

• It must be zero

How do you solve the inequality 5 - 2x ≥ 0 for the domain of a square root function?

• Multiply both sides by 2

• Divide both sides by 5

• Subtract 5 from both sides and divide by -2

• Add 5 to both sides and divide by 2

What is the domain of the function f(x) = √(5 - 2x) in interval notation?

• [0, ∞)

• (-∞, 5/2)

• [5/2, ∞)

• (-∞, 5/2]

For a natural logarithm function, what must be true about the argument?

• It must be non-negative

• It must be negative

• It must be zero

• It must be positive

How do you solve the inequality 5 - 2x > 0 for the domain of a natural log function?

• Add 5 to both sides and divide by 2

• Subtract 5 from both sides and divide by -2

• Subtract 5 from both sides and divide by 2

• Multiply both sides by 5

What is the domain of the function f(x) = ln(5 - 2x) in interval notation?

• [5/2, ∞)

• (-∞, 5/2]

• [0, ∞)

• (-∞, 5/2)

What happens to the inequality sign when you divide both sides by a negative number?

• It disappears

• It becomes an equality

• It reverses

• It stays the same