Domain of a function

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

How do you express the domain of a function using interval notation?

Back

Interval notation uses parentheses and brackets to denote open and closed intervals. For example, (a, b) means all numbers between a and b, not including a and b, while [a, b] includes a and b.

Front

What does it mean if a function has a domain of (-∞, a) U (a, ∞)?

Back

It means the function is defined for all real numbers except for the value 'a'.

Front

If a function has a domain of [-1, ∞), what does this indicate?

Back

This indicates that the function is defined for all real numbers starting from -1 and including -1, extending to positive infinity.

Front

What is the domain of the function f(x) = 1/(x-3)?

Back

The domain is (-∞, 3) U (3, ∞) because the function is undefined at x = 3.

Front

How do you find the domain of a polynomial function?

Back

The domain of a polynomial function is all real numbers, as polynomials are defined for every real number.

Front

What is the domain of the function f(x) = √(x-4)?

Back

The domain is [4, ∞) because the expression under the square root must be non-negative.

Front

If a function has a domain of (a, b), what can be said about the endpoints a and b?

Back

The endpoints a and b are not included in the domain, meaning the function is undefined at these points.

Front

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

Back

The domain is (0, ∞) because the logarithm is only defined for positive real numbers.

Front

How do you determine the domain of a rational function?

Back

To find the domain of a rational function, identify values that make the denominator zero and exclude them from the domain.