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.

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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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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.

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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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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.

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.

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.

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.