Domain and Range (15)

Front

What is the definition of range in a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is the definition of domain in 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

What does it mean if a function is 'even'?

Back

A function is even if f(-x) = f(x) for all x in the domain, meaning its graph is symmetric about the y-axis.

Front

What does it mean if a function is 'odd'?

Back

A function is odd if f(-x) = -f(x) for all x in the domain, meaning its graph is symmetric about the origin.

Front

What is the notation for an open interval?

Back

An open interval is denoted by parentheses, e.g., (a, b) means a < x < b.

Front

What is the notation for a closed interval?

Back

A closed interval is denoted by brackets, e.g., [a, b] means a ≤ x ≤ b.

Front

What is the notation for a half-open interval?

Back

A half-open interval is denoted by a combination of brackets and parentheses, e.g., [a, b) means a ≤ x < b.

Front

How do you express the range of a function using set notation?

Back

The range can be expressed in set notation as {y | y is a possible output of the function}.

Front

What is the range of the function f(x) = x^2?

Back

The range of f(x) = x^2 is [0, +∞) because the output is always non-negative.

Front

What is the range of the function f(x) = sin(x)?

Back

The range of f(x) = sin(x) is [-1, 1] because sine values oscillate between -1 and 1.