Domain and Restrictions of Functions

Nancy explains how to find the domain of various types of functions, including polynomials, fractions, and those involving square roots. She covers the necessary steps to determine the domain, such as setting denominators not equal to zero and ensuring radicands are non-negative. The video provides examples and interval notation for clarity.

What is the domain of a function?

• The output of a function

• All possible x values of a function

• All possible y values of a function

• The range of a function

What is the domain of a polynomial function like x^2 + 3x + 1?

• All real numbers

• x > 0

• x < 0

• x ≠ 0

How do you find the domain of a function with a fraction?

• Set the denominator not equal to zero

• Set the numerator equal to zero

• Set the denominator equal to zero

• Set the entire fraction equal to zero

If the denominator of a fraction is x^2 + 5x + 6, what are the restrictions on x?

• x cannot be 0

• x cannot be -3 or -2

• x cannot be 3 or 2

• x cannot be 5 or 6

What is the domain of a function with a denominator x^2 + 3?

• All real numbers

• x cannot be 3

• x cannot be -3

• x cannot be 0

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

• Set the radicand less than zero

• Set the radicand greater than or equal to zero

• Set the radicand equal to zero

• Set the radicand greater than zero

For a square root function with radicand x + 1, what is the domain?

• x ≤ 1

• x ≥ -1

• x < -1

• x > 1

What is the domain of a function with a quadratic expression under a square root?

• x can be any real number

• x can be less than or equal to -3 or greater than or equal to -2

• x can be greater than or equal to -3 and less than or equal to -2

• x can be less than or equal to 3 or greater than or equal to 2

How do you find the domain of a function with a square root in the denominator?

• Set the radicand less than zero

• Set the radicand not equal to zero

• Set the radicand greater than zero

• Set the radicand equal to zero

For a function with a square root in the denominator and radicand x + 1, what is the domain?

• x > -1

• x < -1

• x ≤ -1

• x ≥ -1