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

Front

Identify if the following set is a function: (2,3), (3,4), (2,5)

Back

Not a function, because the input '2' is related to two different outputs (3 and 5).

Front

Identify if the following set is a function: (1,2), (2,3), (3,4)

Back

Function, because each input is related to exactly one output.

Front

What is a relation?

Back

A relation is a set of ordered pairs, which can include functions but does not have to.

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 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, and no two different inputs share the same output.

Front

Is the following graph a function? (Graph showing a vertical line intersecting at two points)

Back

Not a function, because it fails the vertical line test.

Front

Is the following graph a function? (Graph showing a line with no vertical intersections)

Back

Function, because it passes the vertical line test.

Front

What is the definition of a domain in a function?

Back

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