Average Rate of Change
Flashcard
•
Mathematics
•
9th Grade
•
Hard
+1
Standards-aligned
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1.
FLASHCARD QUESTION
Front
What is the average rate of change (ARC)?
Back
The average rate of change (ARC) of a function over an interval [x1, x2] is defined as the change in the function's value divided by the change in the input value, calculated as (f(x2) - f(x1)) / (x2 - x1).
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 the function f(x) = 2x^2 + 12x + 16 on the interval [-3, -2]?
Back
First, calculate f(-3) and f(-2). Then, use the formula ARC = (f(-2) - f(-3)) / (-2 - (-3)). The result is 2.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
3.
FLASHCARD QUESTION
Front
What is the formula for average rate of change?
Back
The formula for average rate of change is (y2 - y1) / (x2 - x1).
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
4.
FLASHCARD QUESTION
Front
If f(x) = x^2, what is the average rate of change from x = 1 to x = 3?
Back
The average rate of change is (f(3) - f(1)) / (3 - 1) = (9 - 1) / (3 - 1) = 4.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
5.
FLASHCARD QUESTION
Front
What does a positive average rate of change indicate about a function?
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
6.
FLASHCARD QUESTION
Front
What does a negative average rate of change indicate about a function?
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
7.
FLASHCARD QUESTION
Front
If the average rate of change is zero, what can be inferred about the function?
Back
If the average rate of change is zero, it indicates that the function's value does not change over the interval, suggesting it is constant.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
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