Intervals of Graphs

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What is an interval in a graph?

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An interval in a graph is a range of values on the x-axis or y-axis that indicates where a function is defined or where certain properties hold.

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CCSS.HSF-IF.C.7E

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What does a constant interval mean?

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A constant interval means that the value of the function does not change over that range of x-values.

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CCSS.HSF-LE.A.1B

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How do you identify increasing intervals on a graph?

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Increasing intervals are identified where the graph rises as you move from left to right.

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How do you identify decreasing intervals on a graph?

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Decreasing intervals are identified where the graph falls as you move from left to right.

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What is the significance of the x-axis on a graph?

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The x-axis typically represents the independent variable in a function, often indicating time or quantity.

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

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What is the significance of the y-axis on a graph?

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The y-axis typically represents the dependent variable in a function, showing the output or result of the independent variable.

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

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What does it mean for a graph to be constant over an interval?

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It means that the function's output value remains the same for all input values within that interval.

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CCSS.HSF.IF.B.4

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How can you determine the length of an interval on a graph?

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The length of an interval can be determined by subtracting the lower bound from the upper bound of the interval.

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CCSS.HSA.CED.A.3

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What is a closed interval?

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A closed interval includes its endpoints, denoted as [a, b], meaning both a and b are part of the interval.

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CCSS.6.EE.B.8

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What is an open interval?

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An open interval does not include its endpoints, denoted as (a, b), meaning a and b are not part of the interval.