Identify Functions

Front

What is a function in mathematics?

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

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on a graph.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a graph of a function. If any vertical line intersects the graph at more than one point, then the graph does not represent a function.

Front

What does it mean if a graph does not represent a function?

Back

If a graph does not represent a function, it means that at least one input corresponds to multiple outputs.

Front

What is 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

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

Back

An example of a relation that is not a function is y^2 = x, where each positive x-value corresponds to two y-values (positive and negative).

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.

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What is a many-to-one function?

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

Front

What is a function table?

Back

A function table is a table that displays pairs of input and output values for a function.

Front

How can you tell if a function table represents a function?

Back

A function table represents a function if each input value is unique and corresponds to only one output value.