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G G G G G G G G G G
Ch.G2 FunctionsGandGGraphs
2.1 BasicsGofGFunctionsGandGTheirGGraphs
1 FindG theG DomainG andG RangeG ofG aG Relation
MULTIPLEG CHOICE.G ChooseG theG oneG alternativeG thatG bestG completesG theG statementG orG answersG theG question.
GiveG theG domainG andG rangeG ofG theG relation.
1)G {(-5,G -5),G (-2,G -6),G (12,G 7),G (12,G -8)}
A) domainG =G{-5,G 12,G -2};G rangeG =G{-5,G 7,G -6,G -8}
B) domainG =G{-5,G 7,G -6,G -8};G rangeG =G{-5,G 12,G -2}
C) domainG =G{-5,G 12,G -2,G 22};G rangeG =G{-5,G 7,G -6,G -8}
D) domainG =G{-5,G 12,G -2,G -12};G rangeG =G{-5,G 7,G -6,G -8}
2)G {(-2,G -8),G (12,G 5),G (2,G 1),G (2,G -5)}
A) domainG =G{2,G -2,G 12};G rangeG =G{1,G -8,G 5,G -5} B)G domainG =G{2,G -2,G 12,G -2};G rangeG =G{1,G -8,G 5,G -5}
C)G domainG =G{2,G -2,G 12,G 12};G rangeG =G{1,G -8,G 5,G -5} D)G domainG =G{1,G -8,G 5,G -5};G rangeG =G{2,G -2,G 12}
3)G {(4,G 4),G (-9,G 8),G (7,G 1),G (-7,G -5)}
A) domainG=G{-7,G 4,G 7,G-9};GrangeG=G{-5,G 4,G 1,G 8}
B) domainG=G{-5,G 4,G 1,G 8};GrangeG=G{-7,G 4,G 7,G -9}
C) domainG =G{-7,G 4,G 7,G -9};G rangeG =G{-5,G -4,G 4,G 1,G 8}
D) domainG =G{-7,G 4,G 7,G -9};G rangeG =G{-5,G -5,G 4,G 1,G 8}
4)G {(-12,G 8),G (-12,G -5),G (-3,G 2),G (-10,G -8),G (6,G 3)}
A) domainG =G{-10,G 6,G -12,G -3};G rangeG =G{-8,G 3,G -5,G 2,G 8}
B) domainG =G{-10,G -4,G 6,G -12,G -3};G rangeG =G{-8,G 3,G -5,G 2,G 8}
C) domainG =G{-10,G 14,G 6,G -12,G -3};G rangeG =G{-8,G 3,G -5,G 2,G 8}
D) domainG =G{-8,G 3,G -5,G 2,G 8};G rangeG =G{-10,G -10,G 6,G -12,G -3}
5)G {(-1,G -4),G (-2,G -3),G (-2,G 0),G (7,G 3),G (23,G 5)}
A) domain:G {-1,G 7,G -2,G 23};G range:G {-4,G -3,G 0,G 3,G 5} B)G domain:G {-4,G -3,G 3,G 5};G range:G {-1,G 7,G -2,G 23}
C)G domain:G {-4,G -3,G 0,G 3,G 5};G range:G {-1,G 7,G -2,G 23} D)G domain:G {-1,G 7,G -2,G 23};G range:G {-4,G -3,G 3,G 5}
6)G {(-4,G -8),G (-12,G 8),G (-10,G 1),G (3,G -3),G (4,G 9)}
A) domainG =G{4,G -12,G 3,G -4,G -10};G rangeG =G{9,G 8,G -3,G -8,G 1}
B) domainG =G{9,G 8,G -3,G -8,G 1};G rangeG =G{4,G -12,G 3,G -4,G -10}
C) domainG =G{4,G 9,G -12,G 8,G 3};G rangeG =G{-3,G -4,G -8,G -10,G 1}
D) domainG =G{-3,G -4,G -8,G -10,G 1};G rangeG =G{4,G 9,G -12,G 8,G 3}
7)G {(-4,G 13),G (-3,G 6),G (0,G -3),G (3,G 6),G (5,G 22)}
A) domain:G {-4,G -3,G 0,G 3,G 5};G range:G {13,G 6,G -3,G 22} B)G domain:G {-4,G -3,G 3,G 5};G range:G {13,G 6,G -3,G 22}
C)G domain:G {13,G 6,G -3,G 22};G range:G {-4,G -3,G 0,G 3,G 5} D)G domain:G {13,G 6,G -3,G 22};G range:G {-4,G -3,G 3,G 5}
2 DetermineG WhetherG aG RelationG isG aG Function
MULTIPLEG CHOICE.G ChooseG theG oneG alternativeG thatG bestG completesG theG statementG orG answersG theG question.
DetermineG whetherG theG relationG isG aG function.
1)G {(-3,G 2),G (3,G -1),G (4,G 7),G (7,G -5),G (11,G 4)}
A) Function B)G NotGaGfunction
2)G {(-6,G -3),G (-2,G 3),G (-1,G -8),G (-1,G 8)}
A) NotGaGfunction B)G Function
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G G G G G G G G G G
3)G {(-9,G 9),G (-9,G -1),G (2,G -8),G (5,G 4),G (10,G -9)}
A) NotGaGfunction B)G Function
4)G {(3,G -1),G (3,G 8),G (5,G -6),G (7,G 3),G (11,G -2)}
A) NotGaGfunction B)G Function
5)G {(-4,G 1),G (-1,G -9),G (1,G -3),G (5,G -6)}
A) Function B)G NotGaGfunction
6)G {(-9,G 5),G (-9,G -4),G (1,G -6),G (5,G -5),G (8,G -2)}
A) NotGaGfunction B)G Function
7)G {(-6,G -9),G (-4,G -8),G (1,G 6),G (3,G -9)}
A) Function B)G NotGaGfunction
8)G {(-6,G 3),G (-1,G -1),G (3,G -1),G (3,G -2)}
A) NotGaGfunction B)G Function
9)G {(-5,G 3),G (-2,G -2),G (4,G 5),G (8,G 9)}
A) Function B)G NotGaGfunction
10)G {(-3,G 7),G (2,G -9),G (4,G 1),G (8,G 5),G (11,G -1)}
A) Function B)G NotGaGfunction
3 DetermineG WhetherG anG EquationG RepresentsG aG Function
MULTIPLEG CHOICE.G ChooseG theG oneG alternativeG thatG bestG completesG theG statementG orG answersG theG question.
DetermineG whetherG theG equationG definesG yG asG aG functionG ofG x.
1) xG+GyG=G81
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
2) 6xG+G6yG=G11
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
3) x2G+GyG=G4
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
4) xG+Gy2G =G49
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
5) x2G+Gy2G=G16
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
6) y2G=G3x
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
7) xG=Gy2
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
8) yG=Gx3
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
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G G G G G G G G G G
9) yG=G-G xG+G6
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
10) yG=G -6xG+G5
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
11) xG+Gy3G =G1
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
12) xyG +G6yG=G1
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
13) |x|G-GyG=G2
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
4 EvaluateG aG Function
MULTIPLEG CHOICE.G ChooseG theG oneG alternativeG thatG bestG completesG theG statementG orG answersG theG question.
EvaluateG theG functionG atG theG givenG valueG ofG theG independentG variableG andG simplify.
1) f(x)G =G-6xG -G5; f(-3)
A) 13 B)G 33 C)G 23 D)G -11
2) f(x)G =Gx2G +G3; f(xG +G4)
2
A) x +G8xG+G19
G B)G x2G +G16 C)G x2G +G8xG+G16 D)G x2G +G7
3) f(x)G=G3x2G -G3xG-G5;G G f(xG -G1)
A) 3x2G -G9xG+G1 B)G -9x2G +G3xG +G1 C)G 3x2G -G9xG-G5 D)G 3x2G -G18xG-G5
4) g(x)G =G2xG +G4; g(xG-G1)
A) 2xG+G2 B)G2xG+G4 C)G 2xG+G1 G
D)G
1G
xG+G4
G2
5) h(x)G=GxG-G3G; h(16)
A) 13 B)G -19 C)G 19 D)G -13
6) f(x)G=G xG+G20; f(-4)
A) 4 B)G -4 C)G 2 D)G notGaGrealGnumber
x2G-G7G
7) f(x)G=G ;G G f(4)
x3G -G2x
G 9G G9 G9 G2
A) B) G C) G D)
56 64 62 7
x3G+G6G
8) f(x)G=G ;
f(4)
Gx2G+G4
35 16 G11
7
G B)
G
C)
G D)G
A) 8 5 10
2
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G G G G G G G G G G
SolveG theG problem.
9) TheGfunctionGP(x)G=G0.6xG-
G89GmodelsGtheGrelationshipGbetweenGtheGnumberGofGpretzelsGxGthatGaGcertainGvendorGsellsGandGtheGprof
itGtheGvendorGmakes.GFindGP(500),GtheGprofitGtheGvendorGmakesGfromGsellingG500Gpretzels.
A) $211 B)G $300 C)G $389 D)G $411
10) TheGtotalGcostGinGdollarsGforGaGcertainGcompanyGtoGproduceGxGemptyGjarsGtoGbeGusedGbyGaGjellyGproduc
erGisGgivenGbyGtheGfunctionGC(x)G=G0.5xG+G20,000.GFindG C(50,000),GtheGcostGofGproducingG50,000G jars.
A) $45,000 B)G $25,000 C)G $20.50 D)G $50,020
PageG 4
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G G G G G G G G G G
Ch.G2 FunctionsGandGGraphs
2.1 BasicsGofGFunctionsGandGTheirGGraphs
1 FindG theG DomainG andG RangeG ofG aG Relation
MULTIPLEG CHOICE.G ChooseG theG oneG alternativeG thatG bestG completesG theG statementG orG answersG theG question.
GiveG theG domainG andG rangeG ofG theG relation.
1)G {(-5,G -5),G (-2,G -6),G (12,G 7),G (12,G -8)}
A) domainG =G{-5,G 12,G -2};G rangeG =G{-5,G 7,G -6,G -8}
B) domainG =G{-5,G 7,G -6,G -8};G rangeG =G{-5,G 12,G -2}
C) domainG =G{-5,G 12,G -2,G 22};G rangeG =G{-5,G 7,G -6,G -8}
D) domainG =G{-5,G 12,G -2,G -12};G rangeG =G{-5,G 7,G -6,G -8}
2)G {(-2,G -8),G (12,G 5),G (2,G 1),G (2,G -5)}
A) domainG =G{2,G -2,G 12};G rangeG =G{1,G -8,G 5,G -5} B)G domainG =G{2,G -2,G 12,G -2};G rangeG =G{1,G -8,G 5,G -5}
C)G domainG =G{2,G -2,G 12,G 12};G rangeG =G{1,G -8,G 5,G -5} D)G domainG =G{1,G -8,G 5,G -5};G rangeG =G{2,G -2,G 12}
3)G {(4,G 4),G (-9,G 8),G (7,G 1),G (-7,G -5)}
A) domainG=G{-7,G 4,G 7,G-9};GrangeG=G{-5,G 4,G 1,G 8}
B) domainG=G{-5,G 4,G 1,G 8};GrangeG=G{-7,G 4,G 7,G -9}
C) domainG =G{-7,G 4,G 7,G -9};G rangeG =G{-5,G -4,G 4,G 1,G 8}
D) domainG =G{-7,G 4,G 7,G -9};G rangeG =G{-5,G -5,G 4,G 1,G 8}
4)G {(-12,G 8),G (-12,G -5),G (-3,G 2),G (-10,G -8),G (6,G 3)}
A) domainG =G{-10,G 6,G -12,G -3};G rangeG =G{-8,G 3,G -5,G 2,G 8}
B) domainG =G{-10,G -4,G 6,G -12,G -3};G rangeG =G{-8,G 3,G -5,G 2,G 8}
C) domainG =G{-10,G 14,G 6,G -12,G -3};G rangeG =G{-8,G 3,G -5,G 2,G 8}
D) domainG =G{-8,G 3,G -5,G 2,G 8};G rangeG =G{-10,G -10,G 6,G -12,G -3}
5)G {(-1,G -4),G (-2,G -3),G (-2,G 0),G (7,G 3),G (23,G 5)}
A) domain:G {-1,G 7,G -2,G 23};G range:G {-4,G -3,G 0,G 3,G 5} B)G domain:G {-4,G -3,G 3,G 5};G range:G {-1,G 7,G -2,G 23}
C)G domain:G {-4,G -3,G 0,G 3,G 5};G range:G {-1,G 7,G -2,G 23} D)G domain:G {-1,G 7,G -2,G 23};G range:G {-4,G -3,G 3,G 5}
6)G {(-4,G -8),G (-12,G 8),G (-10,G 1),G (3,G -3),G (4,G 9)}
A) domainG =G{4,G -12,G 3,G -4,G -10};G rangeG =G{9,G 8,G -3,G -8,G 1}
B) domainG =G{9,G 8,G -3,G -8,G 1};G rangeG =G{4,G -12,G 3,G -4,G -10}
C) domainG =G{4,G 9,G -12,G 8,G 3};G rangeG =G{-3,G -4,G -8,G -10,G 1}
D) domainG =G{-3,G -4,G -8,G -10,G 1};G rangeG =G{4,G 9,G -12,G 8,G 3}
7)G {(-4,G 13),G (-3,G 6),G (0,G -3),G (3,G 6),G (5,G 22)}
A) domain:G {-4,G -3,G 0,G 3,G 5};G range:G {13,G 6,G -3,G 22} B)G domain:G {-4,G -3,G 3,G 5};G range:G {13,G 6,G -3,G 22}
C)G domain:G {13,G 6,G -3,G 22};G range:G {-4,G -3,G 0,G 3,G 5} D)G domain:G {13,G 6,G -3,G 22};G range:G {-4,G -3,G 3,G 5}
2 DetermineG WhetherG aG RelationG isG aG Function
MULTIPLEG CHOICE.G ChooseG theG oneG alternativeG thatG bestG completesG theG statementG orG answersG theG question.
DetermineG whetherG theG relationG isG aG function.
1)G {(-3,G 2),G (3,G -1),G (4,G 7),G (7,G -5),G (11,G 4)}
A) Function B)G NotGaGfunction
2)G {(-6,G -3),G (-2,G 3),G (-1,G -8),G (-1,G 8)}
A) NotGaGfunction B)G Function
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G G G G G G G G G G
3)G {(-9,G 9),G (-9,G -1),G (2,G -8),G (5,G 4),G (10,G -9)}
A) NotGaGfunction B)G Function
4)G {(3,G -1),G (3,G 8),G (5,G -6),G (7,G 3),G (11,G -2)}
A) NotGaGfunction B)G Function
5)G {(-4,G 1),G (-1,G -9),G (1,G -3),G (5,G -6)}
A) Function B)G NotGaGfunction
6)G {(-9,G 5),G (-9,G -4),G (1,G -6),G (5,G -5),G (8,G -2)}
A) NotGaGfunction B)G Function
7)G {(-6,G -9),G (-4,G -8),G (1,G 6),G (3,G -9)}
A) Function B)G NotGaGfunction
8)G {(-6,G 3),G (-1,G -1),G (3,G -1),G (3,G -2)}
A) NotGaGfunction B)G Function
9)G {(-5,G 3),G (-2,G -2),G (4,G 5),G (8,G 9)}
A) Function B)G NotGaGfunction
10)G {(-3,G 7),G (2,G -9),G (4,G 1),G (8,G 5),G (11,G -1)}
A) Function B)G NotGaGfunction
3 DetermineG WhetherG anG EquationG RepresentsG aG Function
MULTIPLEG CHOICE.G ChooseG theG oneG alternativeG thatG bestG completesG theG statementG orG answersG theG question.
DetermineG whetherG theG equationG definesG yG asG aG functionG ofG x.
1) xG+GyG=G81
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
2) 6xG+G6yG=G11
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
3) x2G+GyG=G4
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
4) xG+Gy2G =G49
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
5) x2G+Gy2G=G16
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
6) y2G=G3x
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
7) xG=Gy2
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
8) yG=Gx3
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
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G G G G G G G G G G
9) yG=G-G xG+G6
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
10) yG=G -6xG+G5
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
11) xG+Gy3G =G1
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
12) xyG +G6yG=G1
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
13) |x|G-GyG=G2
A) yGisG aG functionG ofG x B)G yGisG notGaGfunctionGofG x
4 EvaluateG aG Function
MULTIPLEG CHOICE.G ChooseG theG oneG alternativeG thatG bestG completesG theG statementG orG answersG theG question.
EvaluateG theG functionG atG theG givenG valueG ofG theG independentG variableG andG simplify.
1) f(x)G =G-6xG -G5; f(-3)
A) 13 B)G 33 C)G 23 D)G -11
2) f(x)G =Gx2G +G3; f(xG +G4)
2
A) x +G8xG+G19
G B)G x2G +G16 C)G x2G +G8xG+G16 D)G x2G +G7
3) f(x)G=G3x2G -G3xG-G5;G G f(xG -G1)
A) 3x2G -G9xG+G1 B)G -9x2G +G3xG +G1 C)G 3x2G -G9xG-G5 D)G 3x2G -G18xG-G5
4) g(x)G =G2xG +G4; g(xG-G1)
A) 2xG+G2 B)G2xG+G4 C)G 2xG+G1 G
D)G
1G
xG+G4
G2
5) h(x)G=GxG-G3G; h(16)
A) 13 B)G -19 C)G 19 D)G -13
6) f(x)G=G xG+G20; f(-4)
A) 4 B)G -4 C)G 2 D)G notGaGrealGnumber
x2G-G7G
7) f(x)G=G ;G G f(4)
x3G -G2x
G 9G G9 G9 G2
A) B) G C) G D)
56 64 62 7
x3G+G6G
8) f(x)G=G ;
f(4)
Gx2G+G4
35 16 G11
7
G B)
G
C)
G D)G
A) 8 5 10
2
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G G G G G G G G G G
SolveG theG problem.
9) TheGfunctionGP(x)G=G0.6xG-
G89GmodelsGtheGrelationshipGbetweenGtheGnumberGofGpretzelsGxGthatGaGcertainGvendorGsellsGandGtheGprof
itGtheGvendorGmakes.GFindGP(500),GtheGprofitGtheGvendorGmakesGfromGsellingG500Gpretzels.
A) $211 B)G $300 C)G $389 D)G $411
10) TheGtotalGcostGinGdollarsGforGaGcertainGcompanyGtoGproduceGxGemptyGjarsGtoGbeGusedGbyGaGjellyGproduc
erGisGgivenGbyGtheGfunctionGC(x)G=G0.5xG+G20,000.GFindG C(50,000),GtheGcostGofGproducingG50,000G jars.
A) $45,000 B)G $25,000 C)G $20.50 D)G $50,020
PageG 4
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