Refine: Analyzing Functional Relationships Qualitatively

Front

What is a qualitative description of a function?

Back

A qualitative description of a function provides information about the general behavior of the function, such as whether it is increasing or decreasing, but does not include specific numerical values or rates of change.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What information about a function is NOT provided by a qualitative description?

Back

The rate of change for each linear section of the graph.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What does it mean for a function to be increasing at a constant rate?

Back

It means that for every equal increase in the input (x), the output (y) increases by the same amount.

Tags

CCSS.HSF-LE.A.1B

Front

What does it mean for a function to be increasing at a varying rate?

Back

It means that the amount by which the output (y) increases changes as the input (x) increases.

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CCSS.HSF.IF.B.4

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What is the difference between a constant rate of change and a varying rate of change?

Back

A constant rate of change means the function's output changes by the same amount for equal changes in input, while a varying rate of change means the output changes by different amounts for equal changes in input.

Tags

CCSS.HSF-LE.A.1B

Front

How can you determine if a function is decreasing?

Back

A function is decreasing if, as the input (x) increases, the output (y) decreases.

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What does it mean for a function to be linear?

Back

A linear function has a constant rate of change and can be represented by a straight line on a graph.

Tags

CCSS.HSF-LE.A.1B

Front

What does it mean for a function to be nonlinear?

Back

A nonlinear function does not have a constant rate of change and can be represented by a curve on a graph.

Tags

CCSS.8.F.A.3

Front

What is the significance of intervals in analyzing functions?

Back

Intervals help identify where a function is increasing, decreasing, or constant, allowing for a better understanding of its overall behavior.

Front

What is a graph's direction in each interval?

Back

The direction indicates whether the function is increasing, decreasing, or constant in that specific interval.