Increasing & Decreasing Functions
Authored by S.K. Batra
Mathematics
12th Grade
CCSS covered
Used 184+ times
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About
This quiz focuses on analyzing the behavior of functions, specifically identifying where functions are increasing, decreasing, or constant across different intervals. The content is appropriate for grade 12 students who are studying advanced functions and introductory calculus concepts. Students need a solid understanding of function notation, interval notation, and the relationship between a function's derivative and its increasing or decreasing behavior. The core mathematical reasoning involves interpreting graphs to identify function behavior, understanding that f'(x) > 0 indicates increasing intervals while f'(x) < 0 indicates decreasing intervals, and applying calculus techniques to find critical points and analyze polynomial functions. Students must also demonstrate fluency with algebraic manipulation when finding derivatives and solving inequalities to determine intervals of increase and decrease. Created by S.K. Batra, a Mathematics teacher in India who teaches grade 12. This assessment serves as an excellent tool for evaluating student mastery of function analysis before advancing to more complex calculus applications. Teachers can utilize this quiz as a diagnostic assessment to identify gaps in student understanding of derivative applications, or as a review activity before unit exams covering related rates and optimization problems. The varied question formats make it suitable for both formative assessment during instruction and summative evaluation of student progress. This quiz aligns with Common Core standards F-IF.B.4 for interpreting key features of graphs and functions, and A-CED.A.3 for representing constraints by systems of functions, while also supporting the mathematical practices of reasoning abstractly and attending to precision in mathematical communication.
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10 questions
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1.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
When is this function increasing?
Tags
CCSS.HSF-IF.C.7A
2.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Over what interval is this function constant?
Tags
CCSS.HSF-IF.C.7B
3.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
List the types of intervals that the graph demonstrates in order.
Tags
CCSS.HSF.IF.B.4
4.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Given a function, f(x), if f'(x)<0 over a certain interval, then f(x) is ____________ over that interval.
Tags
CCSS.HSF.IF.B.4
5.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
What are the intervals on which f(x) = 2x4- 4x2 + 1 is strictly increasing?
(-1,0)
(0,1)
(-∞,-1) and (1,∞)
(-1,0) and (1, ∞)
Tags
CCSS.HSF.IF.B.4
CCSS.HSF.IF.C.7
6.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Let f be the function with derivative given by f'(x) = x2 - 2/x. On which of the following intervals is f decreasing? (No Calculator)
Tags
CCSS.HSA.APR.B.3
7.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
If given f'(x) how would you find the intervals which the graph f(x) has a positive slope?
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