AP PreCalc 2.7-2.8 composite and invertible functions
Mathematics
9th - 12th Grade
CCSS covered
Used 59+ times
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This quiz focuses on composite and inverse functions, fundamental concepts in Advanced Placement Precalculus that typically challenge 11th and 12th grade students. The assessment thoroughly examines students' ability to perform function operations including addition, subtraction, and composition of functions, as well as their understanding of inverse function properties and calculations. Students must demonstrate mastery of function notation, the ability to evaluate nested compositions like f(g(x)) and more complex chains such as h(f(g(x))), and skill in finding inverse functions both algebraically and graphically. The problems require students to understand that finding an inverse involves switching x and y coordinates, recognize that a function's domain equals its inverse's range, determine when functions are invertible using the horizontal line test, and work fluidly between algebraic expressions, tables, and graphical representations of functions. This quiz was created by a classroom teacher who designed it for students studying Advanced Placement Precalculus in grades 9-12. The assessment serves multiple instructional purposes, functioning effectively as targeted practice for students learning composite and inverse function concepts, homework assignments that reinforce classroom instruction, or formative assessment to gauge student understanding before summative evaluations. Teachers can utilize individual sections for warm-up activities focusing on specific skills like basic composition or inverse evaluation, while the complete quiz provides comprehensive review coverage. The problems align with Common Core standards HSF-BF.B.4 (finding inverse functions and verifying inverse relationships) and HSF-BF.A.1 (combining functions using arithmetic operations and composition), supporting the rigorous mathematical reasoning and problem-solving skills essential for success in Advanced Placement Precalculus coursework.
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29 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
all of these
2.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
When f(x) = x2+9 and g(x) = x-9, find f(x)-g(x).
Tags
CCSS.HSF-BF.A.1B
3.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
g(x) = 2x - 5
h(x) = 4x + 5
Find (g - h)(3)
18
16
-16
28
Tags
CCSS.HSF-BF.A.1B
4.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
p(x) = 3x + 4
q(x) = 2x2
Find p(p(-3))
Tags
CCSS.HSF-BF.A.1C
5.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
p(x) = 3x + 4
q(x) = 2x2
Find p(q(x))
Tags
CCSS.HSF-BF.A.1C
6.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))
Tags
CCSS.HSF-BF.A.1C
7.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Find the inverse of f(x) = -4x - 12
Tags
CCSS.HSF-BF.B.4A
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