What is the formula for calculating the slope of a line?

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1) for two points (x1, y1) and (x2, y2) on the line.

What is the difference between average rate of change and instantaneous rate of change?

The average rate of change measures the change over an interval, while the instantaneous rate of change measures the change at a specific point.

How do you find the average rate of change from a graph?

To find the average rate of change from a graph, identify two points on the curve, then use the formula (y2 - y1) / (x2 - x1).

What is the role of intervals in determining average rate of change?

Intervals define the specific range over which the average rate of change is calculated, affecting the result based on the function's behavior.

Can a function be both linear and non-linear?

No, a function cannot be both linear and non-linear; it must fit one definition based on its graph.

What is a piecewise function?

A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the domain.

How does the average rate of change relate to the concept of derivatives?

The average rate of change over an interval approaches the instantaneous rate of change (derivative) as the interval shrinks to zero.

What is the importance of understanding average rates of change in real-world applications?

Understanding average rates of change is crucial for analyzing trends, making predictions, and solving problems in various fields such as physics, economics, and biology.

Graded - Average Rate of Change of Non-Linear Functions

Flashcard

•

Mathematics

•

8th - 9th Grade

•

Practice Problem

•

Hard

•

CCSS

8.F.B.4, 8.F.A.3, 8.EE.B.5

Standards-aligned

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15 questions

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FLASHCARD QUESTION

Front

What is the average rate of change of a function over an interval?

Back

The average rate of change of a function over an interval [a, b] is calculated as (f(b) - f(a)) / (b - a).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

FLASHCARD QUESTION

Front

How do you determine if a function is linear?

Back

A function is linear if its graph is a straight line, which means the rate of change is constant throughout the interval.

Tags

CCSS.8.F.A.3

FLASHCARD QUESTION

Front

What is a non-linear function?

Back

A non-linear function is a function whose graph is not a straight line, indicating that the rate of change varies over the interval.

Tags

CCSS.8.F.A.3

FLASHCARD QUESTION

Front

What does a negative average rate of change indicate?

Back

A negative average rate of change indicates that the function is decreasing over the interval.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

FLASHCARD QUESTION

Front

What does a positive average rate of change indicate?

Back

A positive average rate of change indicates that the function is increasing over the interval.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

FLASHCARD QUESTION

Front

How can you visually identify a non-linear function on a graph?

Back

A non-linear function can be identified by its curved graph, which does not form a straight line.

Tags

CCSS.8.F.A.3

FLASHCARD QUESTION

Front

What is the significance of the slope in a linear function?

Back

The slope of a linear function represents the constant rate of change between the dependent and independent variables.

Tags

CCSS.8.EE.B.5

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