Finding the Domain of Functions

The video tutorial explains how to determine the domain of functions, focusing on rational and radical functions. It highlights the importance of avoiding values that make the denominator zero in rational functions and ensuring non-negative values under the square root in radical functions. The tutorial provides step-by-step methods to find the domain using factorization and solving inequalities.

What is the domain of a function?

• The set of all possible output values.

• The set of all possible input values.

• The set of all positive numbers.

• The set of all negative numbers.

What is the purpose of finding the domain of a function?

• To find the maximum value of the function.

• To find the minimum value of the function.

• To determine the range of output values.

• To identify the valid input values.

Why must we avoid zero in the denominator of a fraction?

• It makes the function undefined.

• It makes the function negative.

• It has no effect on the function.

• It makes the function positive.

What should be avoided under a square root in a function?

• Even numbers

• Zero

• Positive numbers

• Negative numbers

What happens if a negative number is under a square root?

• The function becomes positive.

• The function becomes negative.

• The function becomes zero.

• The function becomes undefined.

What is the first step in finding the domain of 1/(x^2 - 7x - 30)?

• Multiply by 30.

• Factor the denominator.

• Add 7 to x.

• Subtract 10 from x.

Which values of x make the denominator of 1/(x^2 - 7x - 30) zero?

• x = 10 and x = -3

• x = 3 and x = -10

• x = 7 and x = -30

• x = 0 and x = 7

What is the result of factoring x^2 - 7x - 30?

• (x - 5)(x + 6)

• (x - 10)(x + 3)

• (x + 10)(x - 3)

• (x - 6)(x + 5)

What is the domain of 1/(x^2 - 7x - 30) in interval notation?

• (-∞, 10) ∪ (-3, ∞)

• (-∞, -3) ∪ (10, ∞)

• (-∞, 10) ∪ (10, ∞)

• (-∞, -3) ∪ (-3, 10) ∪ (10, ∞)

How is the domain of √(2x + 3) determined?

• By setting 2x + 3 greater than or equal to zero.

• By setting 2x + 3 not equal to zero.

• By setting 2x + 3 less than zero.

• By setting 2x + 3 equal to zero.