Functions - Identifying Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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 does it mean for a mapping to be a function?

Back

A mapping is a function if every input (or domain value) is paired with exactly one output (or range value).

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but each input must have only one output.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate system, typically written as (x, y).

Front

Is the set {(1, 2), (2, 3), (1, 4)} a function?

Back

No, this set is not a function because the input '1' is associated with two different outputs (2 and 4).

Front

What is the domain of a function?

Back

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

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

If a function is defined as f(x) = 2x + 3, what is f(2)?

Back

f(2) = 2(2) + 3 = 4 + 3 = 7.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.