Functions, Domain & Range

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from its domain.

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

What is the range of a function?

Back

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

Front

How can you determine if a relation is a function?

Back

A relation is a function if no two ordered pairs have the same first element (input) with different second elements (outputs).

Front

What does the notation { x | -1 ≤ x ≤ 6 } represent?

Back

This notation represents the set of all x values such that x is greater than or equal to -1 and less than or equal to 6.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, which assigns each x value a unique y value.

Front

What is the significance of the interval notation [-1, ∞)?

Back

The interval notation [-1, ∞) indicates that the domain includes all real numbers starting from -1 and extending to positive infinity.

Front

What is a vertical line test?

Back

The vertical line test is a method used to determine if a curve is a function; if a vertical line intersects the curve at more than one point, it is not a function.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph over its domain.

Front

What is a piecewise function?

Back

A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the domain.