Domain of Functions with Roots and Fractions

Nancy explains how to find the domain of various types of functions, including polynomials, rational functions, and those involving square roots. She provides step-by-step instructions for determining the domain, using examples to illustrate each case. The video covers the use of interval notation and addresses common scenarios such as fractions and square roots in both the numerator and denominator. Nancy encourages viewers to engage with the content and offers additional resources for further learning.

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

• Numbers greater than zero

• Only negative numbers

• Only positive numbers

• All real numbers

When finding the domain of a function with a fraction, what should you do with the denominator?

• Set it equal to zero

• Set it not equal to zero

• Ignore it

• Set it greater than zero

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

• All real numbers

• x cannot be negative

• x cannot be 3

• x cannot be zero

For a function with a square root, what must the expression under the root be?

• Equal to zero

• Greater than or equal to zero

• Greater than zero

• Less than zero

What is the domain of a function with a square root of x + 1?

• x less than 1

• x greater than 1

• x less than or equal to -1

• x greater than or equal to -1

How do you find the domain of a function with a quadratic expression under a square root?

• Set the expression less than zero

• Set the expression greater than zero

• Set the expression equal to zero

• Set the expression greater than or equal to zero

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

• Expression under the root greater than zero

• Expression under the root less than zero

• Expression under the root equal to zero

• Expression under the root not equal to zero

If a square root is in the numerator of a fraction, what must be true about the expression under the root?

• It must be less than zero

• It must be greater than zero

• It must be greater than or equal to zero

• It must be equal to zero

What additional restriction is there if a square root is in the numerator of a fraction?

• The denominator must be zero

• The numerator must be zero

• The denominator cannot be zero

• The numerator cannot be zero

When finding the domain of a function with a square root in the numerator and a quadratic in the denominator, what should you consider?

• The intersection of restrictions

• The union of restrictions

• Only the numerator

• Only the denominator