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 explored in this Unit 2 Review Answer Key, providing detailed solutions to key concepts. Topics include the identification of functions, independent and dependent variables, and the analysis of graphs. Students preparing for exams will find valuable insights into limits, discontinuities, and asymptotic behavior. This resource is ideal for high school students and educators looking to reinforce understanding of essential pre-calculus principles.

Key Points

  • Analyzes pairs of input and output values to determine function representation.
  • Identifies independent and dependent variables in real-world scenarios.
  • Approximates function values using graphical analysis.
  • Explains the significance of vertical and horizontal asymptotes in function behavior.
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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 are the key characteristics of a function?
A function is defined as a relation where each input corresponds to exactly one output. This means that for any given x-value, there can be no more than one y-value associated with it. In the context of the review, pairs of input and output values are analyzed to determine if they represent a function. If any input has multiple outputs, the relation is not a function.
How do you identify independent and dependent variables?
In a function, the independent variable is the one that is manipulated or changed, while the dependent variable is the outcome that depends on the independent variable. For example, in the context of the hours you stay awake based on the number of Monster drinks consumed, the number of drinks is the independent variable, and the hours awake is the dependent variable.
What is the significance of vertical and horizontal asymptotes?
Vertical asymptotes indicate values where a function approaches infinity or is undefined, often corresponding to discontinuities in the graph. Horizontal asymptotes represent the behavior of a function as x approaches infinity, indicating the value that the function approaches but may never reach. Understanding these concepts is crucial for analyzing the overall behavior of rational functions.
How do you determine if a graph represents a function?
To determine if a graph represents a function, one can use the vertical line test. If a vertical line intersects the graph at more than one point, then the graph does not represent a function. This test is essential for visualizing the relationship between input and output values.
What are discontinuities and how are they classified?
Discontinuities in a function occur when there is a break, jump, or hole in the graph. They can be classified as removable or non-removable. Removable discontinuities occur when a limit exists at that point, but the function is not defined there, while non-removable discontinuities occur when the limit does not exist.

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