Introduction to Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

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) = x^2 for x in [-3, 3].

Back

The domain is -3 ≤ x ≤ 3.

Front

Identify the range of the function: f(x) = x^2 for x in [-3, 3].

Back

The range is 0 ≤ y ≤ 9.

Front

What is an independent variable in a function?

Back

The independent variable is the input value (x) that can be changed freely.

Front

What is a dependent variable in a function?

Back

The dependent variable is the output value (y) that depends on the input value (x).

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 example of a function?

Back

An example of a function is f(x) = 2x + 3.