Domain of Functions and Radicals

This video tutorial explains how to determine the domain of various types of functions, including polynomial, rational, and radical functions. It covers key rules such as not dividing by zero and not taking the square root of negative numbers. The tutorial provides examples and methods for finding domains, including using interval notation and number lines. It also addresses more complex cases involving fractions with radicals.

What is the domain of a function?

• The set of all possible w-values

• The set of all possible y-values

• The set of all possible x-values

• The set of all possible z-values

Which of the following is a rule for finding the domain of a function?

• You can take the square root of a negative number

• You cannot divide by any number

• You can divide by zero

• You cannot take the square root of a negative number

What is the domain of a polynomial function?

• All negative numbers

• All positive numbers

• All real numbers

• All integers

How do you find the domain of a rational function?

• Set the entire function equal to zero

• Set the function greater than zero

• Set the denominator not equal to zero

• Set the numerator equal to zero

What is the domain of a rational function with a denominator of x - 7?

• All real numbers except 7

• All real numbers except -7

• All real numbers

• All real numbers except 0

For a radical function with an even index, what must be true for the expression under the radical?

• 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 is the domain of a radical function with an odd index?

• All positive numbers

• All negative numbers

• All real numbers

• All integers

When a radical appears in the numerator of a fraction, what must be true for the function to be defined?

• The expression under the radical must be greater than zero

• The expression under the radical must be equal to zero

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

• The expression under the radical must be less than zero

What is the domain of a function with a radical in the denominator?

• The expression under the radical must be greater than zero

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

• The expression under the radical must be less than zero

• The expression under the radical must be equal to zero