How to determine the domain of a function with restrictions interval notation

The video tutorial explains how to determine the domain of functions using interval notation, focusing on reciprocal and square root functions. It highlights the importance of identifying 'bad' numbers, such as those that result in division by zero or negative square roots, and demonstrates how to exclude these from the domain. The tutorial provides examples and uses number lines to illustrate the concepts, offering both interval and set notation for clarity.

What is a key restriction when determining the domain of a reciprocal function?

• The function must be linear.

• The numerator must be positive.

• The denominator cannot be zero.

• The function must be continuous.

Why is dividing by zero considered 'bad' when determining the domain?

• It makes the function linear.

• It results in a complex number.

• It simplifies the function.

• It is undefined in mathematics.

How is the domain of a reciprocal function represented on a number line?

• By including only positive numbers.

• By marking only even numbers.

• By excluding the point where the denominator is zero.

• By marking all integers.

What is the domain of the function f(x) = 1/(x-3) in interval notation?

• (-∞, 3]

• (3, ∞)

• [3, ∞)

• (-∞, 3) ∪ (3, ∞)

What condition must be met for a number to be included in the domain of a square root function?

• The number must be zero.

• The number must make the expression under the square root positive.

• The number must be a fraction.

• The number must be negative.

In the function g(x) = sqrt(x-3), what is the domain in interval notation?

• [3, ∞)

• (-∞, 3)

• (-∞, ∞)

• (3, ∞)

How is the domain of a square root function represented in set notation?

• {x | x < 3}

• {x | x > 3}

• {x | x ≤ 3}

• {x | x ≥ 3}