precalc 1.2 flashcard B
Flashcard
•
Mathematics
•
11th Grade
•
Hard
+2
Standards-aligned
Wayground Content
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the difference quotient for a function f(x)?
Back
The difference quotient is defined as (f(x + h) - f(x)) / h, which measures the average rate of change of the function over the interval [x, x + h].
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
2.
FLASHCARD QUESTION
Front
Calculate the difference quotient for f(x) = x^2 - x + 1.
Back
The difference quotient is (f(x + h) - f(x)) / h = ( (x + h)^2 - (x + h) + 1 - (x^2 - x + 1) ) / h = (2x + h - 1) = 2x - 1 + h.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
3.
FLASHCARD QUESTION
Front
What does the term 'average rate of change' refer to in calculus?
Back
The average rate of change of a function over an interval [a, b] is given by (f(b) - f(a)) / (b - a).
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
4.
FLASHCARD QUESTION
Front
What is the derivative of a function?
Back
The derivative of a function at a point is the limit of the difference quotient as h approaches 0, representing the instantaneous rate of change.
5.
FLASHCARD QUESTION
Front
Define the term 'function'.
Back
A function is a relation that assigns exactly one output for each input from a set called the domain.
Tags
CCSS.8.F.A.1
CCSS.HSF.IF.A.1
6.
FLASHCARD QUESTION
Front
What is the significance of the variable 'h' in the difference quotient?
Back
The variable 'h' represents a small change in the input value, used to calculate the average rate of change.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
7.
FLASHCARD QUESTION
Front
Explain the concept of limits in calculus.
Back
A limit is a value that a function approaches as the input approaches some value. It is fundamental in defining derivatives and integrals.
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