Types of 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.

Tags

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 can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

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CCSS.HSF.LE.A.2

CCSS.8.F.B.4

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What is a quadratic function?

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A quadratic function is a function that can be expressed in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0. Its graph is a parabola.

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What is an exponential function?

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An exponential function is a function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent. Its graph increases or decreases rapidly.

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

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

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A quadratic function will show a constant second difference in the y-values when the x-values are equally spaced.

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

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An exponential function will show a constant ratio between consecutive y-values when the x-values are equally spaced.

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CCSS.HSF-LE.A.1A

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What is the general shape of a linear function's graph?

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The graph of a linear function is a straight line.

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CCSS.HSF-IF.C.7A

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What is the general shape of a quadratic function's graph?

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The graph of a quadratic function is a parabola, which can open upwards or downwards.

Tags

CCSS.HSF-IF.C.7A