Asymptote and Holes Practice
Mathematics
10th - 12th Grade
CCSS covered
Used 140+ times
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About
This quiz focuses on rational functions and their key features, specifically asymptotes and holes. The content is appropriate for grades 10-12, covering advanced algebraic concepts that require students to analyze rational expressions and their graphical behavior. Students need a solid foundation in factoring polynomials, simplifying rational expressions, and understanding limits to successfully identify vertical asymptotes, horizontal asymptotes, and removable discontinuities (holes). The problems assess students' ability to distinguish between factors that create asymptotes versus those that create holes, determine horizontal asymptote behavior based on degree relationships between numerator and denominator, and recognize when common factors in the numerator and denominator result in removable discontinuities rather than vertical asymptotes. This quiz was created by a classroom teacher who designed it for students studying rational functions in grades 10-12. The practice problems serve multiple instructional purposes, working effectively as a warm-up activity to activate prior knowledge about rational function behavior, targeted practice for students learning to identify asymptotes and holes, or formative assessment to gauge understanding before moving to more complex graphing tasks. Teachers can assign this as homework to reinforce classroom instruction or use it as a review tool before unit assessments. The quiz aligns with Common Core standards A-APR.6 (rewriting rational expressions) and F-IF.7d (graphing rational functions and identifying key features), as students must analyze the algebraic structure of rational functions to determine their graphical characteristics and understand how factored forms reveal asymptotes and holes.
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7 questions
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1.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Find the horizontal asymptote.
Tags
CCSS.HSF-IF.C.7D
2.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
What are the asymptotes?
Tags
CCSS.HSF-IF.C.7D
3.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Find the vertical asymptotes and holes of the function.
Holes: None;
VA: x = 1, -3
Holes: x = -3;
VA: x = 1
Holes: x = -3, 1
VA: None
Holes: x = 1
VA: x = -3
Tags
CCSS.HSF-IF.C.7D
4.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
What is the hole?
x= 4
x= -4
x= 5
x= -5
Tags
CCSS.HSF-IF.C.7D
5.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Where is the horizontal asymptote?
y= 5
y= 0
y= 1
y= 6
Tags
CCSS.HSF-IF.C.7D
6.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Are there any "holes" in the graph? If so...where?
yes, at x= -1
yes, at x= 1
yes, at x= 0
no
Tags
CCSS.HSF-IF.C.7D
7.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Find the vertical asymptote(s), hole(s) and horizontal asymptote.
Holes: x = 2
H.A.: None
Holes: x = 1
H.A.: None
Holes: x = 2
H.A.: y = 1/4
Holes: x = None
H.A.: None
Tags
CCSS.HSF-IF.C.7D
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