3.1 Relations and Functions- domain and range

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x-value) and an output (y-value).

Front

What is a function?

Back

A function is a special type of relation where each input is associated with exactly one output.

Front

What is the domain of a function?

Back

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

Front

What does it mean for a relation to be a function?

Back

A relation is a function if no two ordered pairs have the same first element (x-value).

Front

Identify the domain of the function f(x) = 2x + 3.

Back

The domain is all real numbers, as there are no restrictions on x.

Front

Identify the range of the function f(x) = x^2.

Back

The range is [0, ∞) because the output (y-value) is always non-negative.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What is an independent variable?

Back

An independent variable is the input value (x) that can be changed freely in a function.

Front

What is a dependent variable?

Back

A dependent variable is the output value (y) that depends on the input value (x) in a function.