Relations and Functions

Front

What is a function?

Back

A function is a relation in which each input (x-value) is associated with exactly one output (y-value).

Front

What is a relation in mathematics?

Back

A relation is any set of ordered pairs, which can include multiple outputs for a single input.

Front

What is the Vertical Line Test?

Back

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

Front

Does the set {(1, 2), (2, 3), (3, 4)} represent y as a function of x?

Back

Yes, it represents y as a function of x because each x-value is unique.

Front

Does the set {(1, 2), (1, 3), (2, 4)} represent y as a function of x?

Back

No, it does not represent y as a function of x because the x-value 1 is associated with two different y-values.

Front

What is the definition of an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) where the first number represents the x-coordinate and the second number represents the y-coordinate.

Front

What does it mean for y to be a function of x?

Back

It means that for every value of x, there is exactly one corresponding value of y.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has 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.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 has two different outputs.