Average Rate of Change

Flashcard
•
Mathematics
•
9th Grade
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the average rate of change of a function f(x) on the interval [a, b]?
Back
The average rate of change of a function f(x) on the interval [a, b] is given by the formula: (f(b) - f(a)) / (b - a).
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
2.
FLASHCARD QUESTION
Front
How do you calculate the average rate of change for f(x) = 2x^2 + 12x + 16 on the interval [-3, -2]?
Back
First, calculate f(-3) and f(-2). Then use the formula: (f(-2) - f(-3)) / (-2 - (-3)). The answer is 2.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
3.
FLASHCARD QUESTION
Front
What does a positive average rate of change indicate about a function on an interval?
Back
A positive average rate of change indicates that the function is increasing on that interval.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
4.
FLASHCARD QUESTION
Front
What does a negative average rate of change indicate about a function on an interval?
Back
A negative average rate of change indicates that the function is decreasing on that interval.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
5.
FLASHCARD QUESTION
Front
If f(x) = 2x^2 + 3x - 1, what is the average rate of change from x = 1 to x = 2?
Back
Calculate f(1) and f(2), then use the formula: (f(2) - f(1)) / (2 - 1). The answer is 9.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
6.
FLASHCARD QUESTION
Front
What is the average rate of change of a linear function?
Back
For a linear function, the average rate of change is constant and equal to the slope of the line.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
7.
FLASHCARD QUESTION
Front
How can you find the average rate of change using a graph?
Back
To find the average rate of change using a graph, identify two points on the curve, (x1, y1) and (x2, y2), and use the formula: (y2 - y1) / (x2 - x1).
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
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