Relations and Functions

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

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

Is the relation {(1,5),(1,7),(3,9),(4,11)} a function?

Back

No, because the input '1' has two different outputs (5 and 7).

Front

Which of the following is NOT a function: {(0,1),(1,2),(2,3),(3,4)} or {(0,2),(1,3),(4,3),(1,2)}?

Back

{(0,2),(1,3),(4,3),(1,2)} is not a function because the input '1' has two different outputs (3 and 2).

Front

What does it mean for a graph to pass the vertical line test?

Back

It means that any vertical line drawn on the graph intersects it at most once.

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.

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) = 2x + 3, where each x-value has a unique y-value.

Front

What is an example of a non-function?

Back

An example of a non-function is the relation {(1,2), (1,3)}, where the input '1' has two outputs.

Front

What is the definition of a one-to-one function?

Back

A one-to-one function is a function where each output is paired with exactly one input.