Function or Not?

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 a non-function?

Back

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

Front

How can you determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

Front

Give an example of a function.

Back

An example of a function is f(x) = 2x + 3, where each input x has a unique output.

Front

Give an example of a non-function.

Back

An example of a non-function is the relation defined by the equation x^2 + y^2 = 1, which relates some x values to multiple y values.

Front

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

Back

A one-to-one relation is a function where each output is related to exactly one input.

Front

What does it mean for a relation to be many-to-one?

Back

A many-to-one relation is a function where multiple inputs can produce the same output.

Front

What is the domain of a function?

Back

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

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.