Identifying 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.

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How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

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 a vertical line crosses the graph more than once, then the graph is not a function.

Front

What is the definition of a domain in a function?

Back

The domain of a function is the complete set of possible values of the independent variable (input).

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What is the definition of a range in a function?

Back

The range of a function is the complete set of possible values of the dependent variable (output).

Front

Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input; each input must correspond to exactly one output.

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What is an example of a function?

Back

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

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

Back

An example of a relation that is not a function is the relation defined by the equation x^2 + y^2 = 1, which gives two outputs for some inputs.

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

Back

A function is one-to-one if it never assigns the same value to two different domain elements; each output is unique to one input.

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What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line, typically in the form f(x) = mx + b.