Domain of Functions with Square Roots

Nancy explains how to find the domain of various types of functions, including polynomials, fractions, and those involving square roots. She covers the basic concept of domain as all possible x values a function can take and provides detailed steps for determining the domain in different scenarios. The video includes examples and explanations of interval notation and restrictions that arise from denominators and radicands. Nancy concludes by encouraging viewers to like the video.

What does the domain of a function represent?

• All possible y values of the function

• All possible x values of the function

• The range of the function

• The maximum value of the function

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

• Only positive numbers

• Only negative numbers

• Numbers greater than zero

• All real numbers

How do you find the domain of a function that is a fraction?

• Set both numerator and denominator not equal to zero

• Set the fraction greater than zero

• Set the denominator not equal to zero

• Set the numerator not equal to zero

If the denominator of a fraction is x^2 + 3, what is the domain?

• x cannot be zero

• x cannot be negative

• All real numbers

• x cannot be 3

What must be true for the expression under a square root in a function?

• It must be equal to zero

• It must be less than zero

• It must be greater than or equal to zero

• It must be greater than zero

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

• x is greater than 1

• x is greater than or equal to -1

• x is less than or equal to -1

• x is less than 1

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

• Set the expression under the root greater than zero

• Set the expression under the root not equal to zero

• Set the expression under the root less than zero

• Set the expression under the root equal to zero

What is the domain of a function with a square root in the numerator and x^2 - 4 in the denominator?

• x less than or equal to 1, x cannot be -2

• x greater than or equal to 1, x cannot be -2

• x less than or equal to -1, x cannot be 2

• x greater than or equal to -1, x cannot be 2

What is the domain of a function with a square root in the numerator?

• The expression under the root must be less than zero

• The expression under the root must be greater than zero

• The expression under the root must be equal to zero

• The expression under the root must be greater than or equal to zero

What is the domain of a function with a square root in the denominator and x + 1 under the root?

• x is less than or equal to -1

• x is greater than or equal to -1

• x is less than -1

• x is greater than -1