Functions

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What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a given set.

Tags

CCSS.8.F.A.1

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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 by checking if any vertical line intersects the graph more than once.

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What does it mean for a relation to be 'not a function'?

Back

A relation is 'not a function' if at least one input is associated with more than one output.

Tags

CCSS.8.F.A.1

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What is an example of a function?

Back

An example of a function is the set of ordered pairs: (1, 2), (2, 3), (3, 4). Each input has a unique output.

Tags

CCSS.8.F.A.1

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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 set of ordered pairs: (1, 2), (1, 3). The input '1' has two different outputs.

Tags

CCSS.8.F.A.1

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What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, described by the equation y = mx + b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What does 'nonproportional' mean in the context of functions?

Back

'Nonproportional' means that the relationship between the variables does not maintain a constant ratio; the graph does not pass through the origin.

Tags

CCSS.8.EE.B.5

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What is a table of values in relation to functions?

Back

A table of values lists pairs of input and output values, helping to visualize the relationship and determine if it is a function.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

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How can you identify a function from a table of values?

Back

You can identify a function from a table of values by ensuring that each input corresponds to exactly one output.

Tags

CCSS.8.F.A.1