Understanding Domains of Functions

The video tutorial explains how to determine the domain of various functions, including quadratic, linear, square root, cube root, constant, cubic, rational, identity, and absolute value functions. It covers the rules for determining domains, such as avoiding division by zero and ensuring non-negative radicands for square roots. The video also demonstrates how to express domains using interval notation and verifies them graphically.

What is the domain of a quadratic function like f(x) = x^2 + 3x - 10?

• All real numbers

• Only positive numbers

• Numbers greater than zero

• Only negative numbers

Which of the following is NOT a rule for determining the domain of a function?

• The domain is all possible x values

• We cannot multiply by zero

• We cannot take the square root of a negative number

• We cannot divide by zero

For the function f(x) = √(36 - 3x), what is the domain?

• x ≤ 12

• x ≥ 12

• x < 12

• x > 12

How do you determine the domain of a square root function?

• Set the radicand greater than or equal to zero

• Set the radicand equal to zero

• Set the radicand less than zero

• Set the radicand not equal to zero

What is the domain of a cube root function like f(x) = ∛(4x - 6)?

• Numbers greater than zero

• Only negative numbers

• Only positive numbers

• All real numbers

Why is the domain of a constant function like f(x) = 19 all real numbers?

• Because the function is linear

• Because the input can be any real number

• Because the output is always the same

• Because the function is not defined

For the rational function f(x) = (x + 1) / (x - 6), what value must be excluded from the domain?

• x = 6

• x = -6

• x = 0

• x = 1

How do you find the domain of a rational function?

• Exclude values that make the numerator zero

• Exclude values that make the denominator zero

• Include only negative values

• Include only positive values

What is the domain of the identity function f(x) = x?

• Only negative numbers

• All real numbers

• Only positive numbers

• Numbers greater than zero

Why is the domain of an absolute value function like f(x) = |x - 3| all real numbers?

• Because absolute value can be taken for any real number

• Because it is a linear function

• Because it is a constant function

• Because it is a quadratic function