Identify Functions (vertical line test)

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

Front

What does it mean if a relation is not a function?

Back

A relation is not a function if at least one input is related to more than one output.

Front

Example of a function: y = 2x + 3. Is this a function?

Back

Yes, this is a function because for every value of x, there is exactly one value of y.

Front

Example of a relation that is not a function: y^2 = x. Is this a function?

Back

No, this is not a function because for some values of x, there are two corresponding values of y.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.

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.

Front

Can a vertical line ever intersect a function's graph more than once?

Back

No, if a vertical line intersects a graph more than once, the graph does not represent a function.

Front

What is an example of a function in real life?

Back

An example of a function in real life is a vending machine: for each button (input), there is one specific item (output) that is dispensed.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is related to exactly one input, meaning no two different inputs produce the same output.