Functions and Limits Pre-Calculus Unit 2 Review Answer Key

Functions and Limits Pre-Calculus Unit 2 Review Answer Key

Functions and Limits in Pre-Calculus are essential topics for understanding mathematical relationships and behaviors. This answer key provides solutions for the Unit 2 Review, which includes function identification, graph analysis, and limit evaluation. It is designed for high school students preparing for exams in Pre-Calculus. Key concepts covered include independent and dependent variables, continuity, and asymptotic behavior. This resource is invaluable for students seeking to reinforce their understanding of functions and limits.

Key Points

  • Includes detailed solutions for function identification and analysis.
  • Covers limit evaluation techniques and continuity concepts.
  • Provides insights into vertical and horizontal asymptotes.
  • Explains the relationship between independent and dependent variables.
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  • MR ALi
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Name:_____________________________Date:_______________Period:_____
Unit2REVIEW–FunctionsandLimits
Pre‐Calculus
1) Dothefollowingpairsofinputandoutputvalues
representafunction:
󰇛
10, 1
󰇜
,
󰇛
4,0
󰇜
,
󰇛
0, 1
󰇜
,
󰇛
3, 2
󰇜
,and
󰇛
4,3
󰇜
?Iftheydon’t,giveaspecific
reasonwhynot.
2)Thehoursyoustayawakeisafunctionofthe
numberof
Monsterdrinksyouhaveintheevening.
Identifytheindependentanddependentvariables.
3)Usethegraphtotherighttoapproximatethe
followingvaluestothenearesttenth.
a.
󰇛
5
󰇜
b.
󰇛
0
󰇜
c.If
󰇛
󰇜
5,then
d.If
󰇛
󰇜
0,thenthepossiblevalue(s)of
are:
4)Ifthedependentvariableisthenumberofkilometersyoucandrive,andtheindependentvariableisthe
amountofgas(measuredinliters)inyourcar,writeasentenceexplainingthemeaningof
󰇛
20
󰇜
285.

5)Tellifthegraphbelowrepresentsafunction.

6)Namethebasicfunctionshownandwritethe
equation.
Function
󰇛
󰇜

7)Identifythedomainintervalswhereeachfunctionis
increasing,decreasing,andconstant.Useinterval
notation.
8)
Domain:
Interval:______________
Inequality:____________
Range:
Interval:______________

Inequality:____________
Inc: Dec:
Constant:

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x
y
x
y

9)Identifythe‐valuesofeachdiscontinuity,andwriteifitis
removableornot.Ifitisnonremovablethenclassifythetype.
10)Givethevalueofeachstatement.
a.
o
)(
lim
1
xf
x
b.
󰇛
2
󰇜
c.
o
)(
lim
1
xf
x
d.
o
)(
lim
2
xf
x
e.
󰇛
1
󰇜
f.
o
)(
lim
2
xf
x
11)Uselimitnotationtorepresentthehorizontaland
verticalasymptotes.
12)
󰇛
󰇜
representsyournumericalgradein
precalculusbasedonthenumberofhoursyou
studyperdayoutsideofschool.Givearelevant
domainandrangeforthisfunctionusinginequality
notation.
 HorizontalAsymptote:
VerticalAsymptote:
13)
󰇛
󰇜


hasaverticalasymptoteat1.Createatableofvaluestodeterminethebehaviorof
thegraphattheverticalasymptote,thenuselimitnotationtoexplainthebehavior.Also,useagraphing
calculatortodeterminethehorizontalasymptote.
14)Sketch(freehand)agraphofafunction
that
satisfiesallofthefollowingconditions:
a.
o
)(
lim
2
xf
x
3
b.
)(
lim
3
xf
x
o

󰇛
2
󰇜
5
c.isincreasingon󰇛, 3󰇜
d.
)(
lim
3
xf
x
o
)(
lim
3
xf
x
o
e.isconstanton󰇛2, 󰇜
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Faqs of Functions and Limits Pre-Calculus Unit 2 Review Answer Key
What types of functions are discussed in the review?
The review discusses various types of functions, including linear, quadratic, and polynomial functions. It emphasizes how to determine if a set of input-output pairs represents a function. Students learn to analyze graphs to identify function behavior, such as increasing, decreasing, and constant intervals.
How does the answer key help with understanding limits?
The answer key provides step-by-step solutions for evaluating limits, including both one-sided and two-sided limits. It illustrates how to apply limit notation and analyze the behavior of functions as they approach specific values. This is crucial for mastering concepts related to continuity and discontinuity in functions.
What is the significance of vertical and horizontal asymptotes?
Vertical and horizontal asymptotes are important concepts in understanding the behavior of functions at extreme values. Vertical asymptotes indicate values where a function approaches infinity, while horizontal asymptotes show the behavior of a function as it extends towards positive or negative infinity. The review explains how to identify these asymptotes through graphical analysis.
What are independent and dependent variables in the context of functions?
In the context of functions, independent variables are the inputs that can be controlled or changed, while dependent variables are the outputs that depend on the values of the independent variables. The review emphasizes the importance of identifying these variables in real-world scenarios, such as the relationship between gas in a car and the distance it can travel.
How can students use this answer key for exam preparation?
Students can use the answer key to verify their understanding of key concepts in functions and limits. By comparing their solutions with the provided answers, they can identify areas of strength and weakness. This resource serves as a study aid to reinforce learning and boost confidence before exams.