Functions

Front

What is a function in mathematics?

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 curve is a graph of a function. If any vertical line intersects the graph at more than one point, then the graph is not a function.

Front

What is the definition of ordered pairs?

Back

Ordered pairs are pairs of numbers used to represent points in a coordinate system, typically written in the form (x, y).

Front

What does it mean for a set of ordered pairs to be a function?

Back

A set of ordered pairs is a function if no two different ordered pairs have the same first element (input).

Front

How can you determine if a table represents a function?

Back

A table represents a function if each input value corresponds to exactly one output value.

Front

What is the output of the function f(x) = 3x - 8 when x = 6?

Back

The output is 10.

Front

What is a non-function?

Back

A non-function is a relation where at least one input is associated with more than one output.

Front

What is the significance of the first element in an ordered pair?

Back

The first element in an ordered pair represents the input value (x-coordinate) in a function.

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 map to only one output.

Front

What is an example of a function?

Back

An example of a function is f(x) = x^2, where each input x has a unique output x^2.