Introduction to Functions

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What is a function?

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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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CCSS.8.F.A.1

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What is a linear function?

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A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is a nonlinear function?

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A nonlinear function is a function that does not graph to a straight line and can include curves, parabolas, and other shapes.

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CCSS.8.F.A.3

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

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A linear function will have a constant rate of change between the x-values and y-values.

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CCSS.HSF-LE.A.1B

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

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CCSS.8.EE.B.5

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What does it mean for a relation to be a function?

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A relation is a function if every input (x-value) has exactly one output (y-value).

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CCSS.8.F.A.1

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What is the y-intercept of a linear function?

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The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

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What is the difference between a function and a non-function?

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A function has one output for each input, while a non-function may have multiple outputs for a single input.

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CCSS.8.F.A.1

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What is an example of a linear function?

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An example of a linear function is y = 2x + 3.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is an example of a nonlinear function?

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An example of a nonlinear function is y = x^2.

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CCSS.8.F.A.3