Name:_________________________________________________Period:___________Date:________________

AnalyzingGraphsofFunctionsandRelationsAssignment

Copyright©PreCalculusCoach.com 1

Useagraphofeachfunctiontoestimatetheindicatedfunctionvalues.

1. 𝒇 𝒙 = −𝒙 + 𝟑𝒇 −𝟏 =? 𝒇 𝟎 =? 𝒇 𝟑 =?

2. 𝒇 𝒙 = 𝒙𝟑 − 𝟑𝒙𝟐 + 𝟐𝒇 −𝟏 =? 𝒇 𝟎 =? 𝒇 𝟐 =?

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚

𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚

𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚

-4 -3 -2 -1 1 2 3 4

-4

-3

-2

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1

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3

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x

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-4 -3 -2 -1 1 2 3 4

-4

-3

-2

-1

1

2

3

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x

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Name:_________________________________________________Period:___________Date:________________

AnalyzingGraphsofFunctionsandRelationsAssignment

Copyright©PreCalculusCoach.com 2

Usethegraphofeachfunctiontoapproximateitsy–intercept.Thenfindthey–interceptalgebraically.

3. 𝒇 𝒙 = 𝒙𝟐 + 𝟐𝒙 + 𝟑 4. 𝒇 𝒙 = 𝒙 + 𝟐 + 𝟐

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚

𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚

5. 𝒇 𝒙 = 𝟐𝒙 − 𝟑 6. 𝒇 𝒙 = 𝒙 + 𝟐

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚

-4 -3 -2 -1 1 2 3 4

-4

-3

-2

-1

1

2

3

4

x

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-4 -3 -2 -1 1 2 3 4

-4

-3

-2

-1

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3

4

x

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-4 -3 -2 -1 1 2 3 4

-4

-3

-2

-1

1

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x

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-4 -3 -2 -1 1 2 3 4

-4

-3

-2

-1

1

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3

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x

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Name:_________________________________________________Period:___________Date:________________

AnalyzingGraphsofFunctionsandRelationsAssignment

Copyright©PreCalculusCoach.com 3

Usethegraphofeachfunctiontoapproximateitszeros.Thenfindthezerosofeachfunctionalgebraically.

7. 𝒇 𝒙 = −𝒙𝟐 − 𝟐𝒙 + 𝟑

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚

8. 𝒇 𝒙 = 𝟐𝒙𝟑 − 𝒙𝟐 − 𝟑𝒙

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚

9. 𝒇 𝒙 = 𝒙𝟑 − 𝟔𝒙𝟐 − 𝟏𝟐𝒙 + 𝟖

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚

-4 -3 -2 -1 1 2 3 4

-4

-3

-2

-1

1

2

3

4

x

y

-4 -3 -2 -1 1 2 3 4

-4

-3

-2

-1

1

2

3

4

x

y

Name:_________________________________________________Period:___________Date:________________

AnalyzingGraphsofFunctionsandRelationsAssignment

Copyright©PreCalculusCoach.com 4

Usethegraphofeachequationtotestforsymmetrywithrespecttothex-axis,y-axis,andtheorigin.Supporttheanswernumerically.Thenconfirmalgebraically.

10. 𝒚 = 𝒙𝟐 + 𝟐

Graphically

SupportNumerically

𝒙

𝒚

(𝒙, 𝒚)

Algebraically

11. 𝒚 = 𝒙𝟑

Graphically

SupportNumerically

𝒙

𝒚

(𝒙, 𝒚)

Algebraically

-4 -3 -2 -1 1 2 3 4

-4

-3

-2

-1

1

2

3

4

x

y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

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x

y

Name:_________________________________________________Period:___________Date:________________

AnalyzingGraphsofFunctionsandRelationsAssignment

Copyright©PreCalculusCoach.com 5

12. 𝟐𝒙𝟐 + 𝟑𝒚𝟐 = 𝟏𝟔

Graphically

Symmetricwithrespectto𝒙-axis

Algebraically

SupportNumerically

𝒙

𝒚

(𝒙, 𝒚)

Symmetricwithrespectto𝒚-axis

Algebraically

SupportNumerically

𝒙

𝒚

(𝒙, 𝒚)

Symmetricwithrespecttoorigin

Algebraically

SupportNumerically

𝒙

𝒚

(𝒙, 𝒚)

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

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x

y

Name:_________________________________________________Period:___________Date:________________

AnalyzingGraphsofFunctionsandRelationsAssignment

Copyright©PreCalculusCoach.com 6

Determinewhetherthefollowingareeven,odd,orneither.

SOLVEREALWORLDPROBLEM

13. 𝒇 𝒙 = 𝒙𝟑 + 𝟐𝒙

14. 𝒈 𝒕 = 𝟐𝒕𝟒 + 𝒕𝟐

15. 𝒉 𝒚 = 𝒚𝟒 − 𝟓𝒚𝟐 − 𝟑𝒚

16. Thetemperature𝑻indegreesFahrenheit𝒕hoursafter6AMisgivenby𝑻 𝒕 = − 𝟏𝟐𝒕𝟐 − 𝟖𝒕 + 𝟑,

𝒇𝒐𝒓𝟎 < 𝒕 < 𝟏𝟎.Find𝑻 𝟎 ,𝑻 𝟐 and𝑻 𝟔 graphicallyandalgebraically.

Graphically

Algebraically

-15 -10 -5 5 10 15

-90

-80

-70

-60

-50

-40

-30

-20

-10

10

20

30

40

50

60

70

80

90

t (h)

T(F)

Name:_________________________________________________Period:___________Date:________________

AnalyzingGraphsofFunctionsandRelationsAssignment

Copyright©PreCalculusCoach.com 7

ANSWERS

Useagraphofeachfunctiontoestimatetheindicatedfunctionvalues.

1. 𝒇 𝒙 = −𝒙 + 𝟑𝒇 −𝟏 =? 𝒇 𝟎 =? 𝒇 𝟑 =?

2. 𝒇 𝒙 = 𝒙𝟑 − 𝟑𝒙𝟐 + 𝟐𝒇 −𝟏 =? 𝒇 𝟎 =? 𝒇 𝟐 =?

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚𝒇 −𝟏 = 𝟒𝒇 𝟎 = 𝟑𝒇 𝟑 = 𝟎

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚𝒇 −𝟏 = −𝟐𝒇 𝟎 = 𝟐𝒇 𝟐 = −𝟐

𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚𝒇 −𝟏 = − −𝟏 + 𝟑 = 𝟏 + 𝟑 = 𝟒𝒇 𝟎 = −𝟎 + 𝟑 = 𝟑𝒇 𝟑 = −𝟑 + 𝟑 = 𝟎

𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚𝒇 −𝟏 = −𝟏 𝟑 − 𝟑 −𝟏 𝟐 + 𝟐 = −𝟏 − 𝟑 + 𝟐 = −𝟐𝒇 𝟎 = 𝟎𝟑 − 𝟑 ∗ 𝟎𝟐 + 𝟐 = 𝟐𝒇 𝟐 = 𝟐𝟑 − 𝟑 ∗ 𝟐𝟐 + 𝟐 = 𝟖 − 𝟏𝟐 + 𝟐 = −𝟐

-4 -3 -2 -1 1 2 3 4

-4

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x

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-4 -3 -2 -1 1 2 3 4

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1

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y

Name:_________________________________________________Period:___________Date:________________

AnalyzingGraphsofFunctionsandRelationsAssignment

Copyright©PreCalculusCoach.com 8

Usethegraphofeachfunctiontoapproximateitsy–intercept.Thenfindthey–interceptalgebraically.

3. 𝒇 𝒙 = 𝒙𝟐 + 𝟐𝒙 + 𝟑 4. 𝒇 𝒙 = 𝒙 + 𝟐 + 𝟐

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚

𝒇 𝒙 = 𝒙𝟐 + 𝟐𝒙 + 𝟑𝒚– 𝐢𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭 = 𝟑𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚𝒚-interceptoccurswhere𝒙 = 𝟎.𝒇 𝟎 = 𝟎𝟐 + 𝟐 ∗ 𝟎 + 𝟑𝒇 𝟎 = 𝟑𝒚– 𝐢𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭 = 𝟑

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚𝒇 𝒙 = 𝒙 + 𝟐 + 𝟐𝒚– 𝐢𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭 ≈ 𝟑. 𝟐𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚𝒚-interceptoccurswhere𝒙 = 𝟎.𝒇 𝟎 = 𝟎 + 𝟐 + 𝟐 = 𝟐 + 𝟐𝒇 𝟎 ≈ 𝟑. 𝟒𝟏𝒚– 𝐢𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭 ≈ 𝟑. 𝟒𝟏

5. 𝒇 𝒙 = 𝟐𝒙 − 𝟑 6. 𝒇 𝒙 = 𝒙 + 𝟐

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚𝒇 𝒙 = 𝟐𝒙 − 𝟑𝒚– 𝐢𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭 = −𝟑𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚𝒚-interceptoccurswhere𝒙 = 𝟎.𝒇 𝟎 = 𝟐 ∗ 𝟎 − 𝟑𝒇 𝟎 = −𝟑𝒚– 𝐢𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭 = −𝟑

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚𝒇 𝒙 = 𝒙 + 𝟐 𝒚– 𝐢𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭 = 𝟐𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚𝒚-interceptoccurswhere𝒙 = 𝟎.𝒇 𝟎 = 𝟎 + 𝟐 𝒇 𝟎 = 𝟐𝒚– 𝐢𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭 = 𝟐

-4 -3 -2 -1 1 2 3 4

-4

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-4 -3 -2 -1 1 2 3 4

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-4 -3 -2 -1 1 2 3 4

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-4 -3 -2 -1 1 2 3 4

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Name:_________________________________________________Period:___________Date:________________

AnalyzingGraphsofFunctionsandRelationsAssignment

Copyright©PreCalculusCoach.com 9

Usethegraphofeachfunctiontoapproximateitszeros.Thenfindthezerosofeachfunctionalgebraically.

7. 𝒇 𝒙 = −𝒙𝟐 − 𝟐𝒙 + 𝟑

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚𝒙 − 𝐢𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭𝐬 − 𝟑𝒂𝒏𝒅𝟏𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚𝒇 𝒙 = 𝟎−𝒙𝟐 − 𝟐𝒙 + 𝟑 = 𝟎(𝒙 + 𝟑) 𝒙 − 𝟏 = 𝟎𝒙 = −𝟑𝒂𝒏𝒅𝒙 = 𝟏𝑻𝒉𝒆𝒛𝒆𝒓𝒐𝒔𝒐𝒇𝒇𝒂𝒓𝒆 − 𝟑𝒂𝒏𝒅𝟏

8. 𝒇 𝒙 = 𝟐𝒙𝟑 − 𝒙𝟐 − 𝟑𝒙

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚𝒙 − 𝐢𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭𝐬 − 𝟏, 𝟎𝒂𝒏𝒅𝟏. 𝟓𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚𝒇 𝒙 = 𝟎𝟐𝒙𝟑 − 𝒙𝟐 − 𝟑𝒙 = 𝟎𝒙(𝒙 + 𝟏) 𝟐𝒙 − 𝟑 = 𝟎𝒙 = −𝟏𝒙 = 𝟎𝒂𝒏𝒅𝒙 = 𝟏. 𝟓𝑻𝒉𝒆𝒛𝒆𝒓𝒐𝒔𝒐𝒇𝒇𝒂𝒓𝒆 − 𝟏, 𝟎𝒂𝒏𝒅𝟏. 𝟓

9. 𝒇 𝒙 = 𝒙𝟑 − 𝟔𝒙𝟐 − 𝟏𝟐𝒙 + 𝟖

𝑮𝒓𝒂𝒑𝒉𝒊𝒄𝒂𝒍𝒍𝒚𝒙 − 𝐢𝐧𝐭𝐞𝐫𝐜𝐞𝐩𝐭𝐬 − 𝟐𝑨𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄𝒂𝒍𝒍𝒚𝒇 𝒙 = 𝟎𝒙𝟑 − 𝟔𝒙𝟐 − 𝟏𝟐𝒙 + 𝟖𝒙 + 𝟐 𝒙 + 𝟐 𝒙 + 𝟐 = 𝒙 + 𝟐 𝟑𝒙 = −𝟐𝑻𝒉𝒆𝒛𝒆𝒓𝒐𝒐𝒇𝒇𝒊𝒔 − 𝟐

-4 -3 -2 -1 1 2 3 4

-4

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-4 -3 -2 -1 1 2 3 4

-4

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Name:_________________________________________________Period:___________Date:________________

AnalyzingGraphsofFunctionsandRelationsAssignment

Copyright©PreCalculusCoach.com 10

Usethegraphofeachequationtotestforsymmetrywithrespecttothex-axis,y-axis,andtheorigin.Supporttheanswernumerically.Thenconfirmalgebraically.

10. 𝒚 = 𝒙𝟐 + 𝟐

Graphically

Thegraphappearstobesymmetricwithrespecttothe𝒚–axisbecause for every point (𝒙, 𝒚)on the graph, there is a point(−𝒙, 𝒚).

SupportNumerically

Thereisatableofvaluestosupportthisconjecture.

𝒙 −𝟐 −𝟏 𝟎 𝟏 𝟐

𝒚 𝟔 𝟑 𝟐 𝟑 𝟔

(𝒙, 𝒚) (−𝟐, 𝟔) (−𝟏, 𝟑) (𝟎, 𝟐) (𝟏, 𝟑) (𝟐, 𝟔)

Algebraically

Because𝒚 = −𝒙 𝟐 + 𝟐isequivalentto 𝒙𝟐 + 𝟐,thegraphissymmetricwithrespecttothe𝒚–axis.

11. 𝒚 = 𝒙𝟑

Graphically

Thegraphappears tobe symmetricwith respect to theoriginbecause for every point (𝒙, 𝒚)on the graph, there is a point(−𝒙,−𝒚).

SupportNumerically

Thereisatableofvaluestosupportthisconjecture.

𝒙 −𝟐 −𝟏 𝟎 𝟏 𝟐

𝒚 − 𝟐𝟑 −𝟏 𝟎 𝟏 𝟐𝟑

(𝒙, 𝒚) (−𝟐,− 𝟐𝟑 ) (−𝟏,−𝟏) (𝟎, 𝟎) (𝟏, 𝟏) (𝟐, 𝟐𝟑 )

Algebraically

Because−𝒚 = −𝒙𝟑 is equivalent to𝒚 = 𝒙𝟑 , the graph issymmetricwithrespecttotheorigin.

-4 -3 -2 -1 1 2 3 4

-4

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Name:_________________________________________________Period:___________Date:________________

AnalyzingGraphsofFunctionsandRelationsAssignment

Copyright©PreCalculusCoach.com 11

12. 𝟐𝒙𝟐 + 𝟑𝒚𝟐 = 𝟏𝟔

Graphically

Thegraphappearstobe:

• symmetricwithrespecttothe𝒙-axisbecauseforeverypoint(𝒙, 𝒚)onthegraph,thereisapoint(𝒙, −𝒚),

• symmetricwithrespecttothe𝒚-axisbecauseforeverypoint(𝒙, 𝒚)onthegraph,thereisapoint(−𝒙, 𝒚),

• symmetricwithrespecttotheoriginbecauseforeverypoint(𝒙, 𝒚)onthegraph,thereisapoint(−𝒙,−𝒚).

Symmetricwithrespectto𝒙-axis

Algebraically

Because 𝟐𝒙𝟐 + 𝟑 −𝒚 𝟐 = 𝟏𝟔 is equivalentto𝟐𝒙𝟐 + 𝟑𝒚𝟐 = 𝟏𝟔, the graph is symmetric withrespectto𝒙-axis.

SupportNumerically

𝒙 𝟐 𝟐 𝟏 𝟏

𝒚 𝟐 𝟔𝟑

−𝟐 𝟔𝟑

−𝟒𝟐𝟑

𝟒𝟐𝟑

(𝒙, 𝒚)

(𝟐,𝟐 𝟔𝟑) (𝟐, −

𝟐 𝟔𝟑) (𝟏, −

𝟒𝟐𝟑) (𝟏,

𝟒𝟐𝟑)

Symmetricwithrespectto𝒚-axis

Algebraically

Because 𝟐 −𝒙 𝟐 + 𝟑𝒚𝟐 = 𝟏𝟔 is equivalentto𝟐𝒙𝟐 + 𝟑𝒚𝟐 = 𝟏𝟔, the graph is symmetric withrespecttothe𝒚–axis.

SupportNumerically

𝒙 −𝟐 −𝟏 𝟏 𝟐

𝒚 𝟐 𝟔𝟑

𝟒𝟐𝟑

𝟒𝟐𝟑

𝟐 𝟔𝟑

(𝒙, 𝒚)

(−𝟐,𝟐 𝟔𝟑) (−𝟏,

𝟒𝟐𝟑) (𝟏,

𝟒𝟐𝟑) (𝟐,

𝟐 𝟔𝟑)

Symmetricwithrespecttoorigin

Algebraically

Because𝟐 −𝒙 𝟐 + 𝟑 −𝒚 𝟐 = 𝟏𝟔 is equivalentto𝟐𝒙𝟐 + 𝟑𝒚𝟐 = 𝟏𝟔, the graph is symmetric withrespecttotheorigin.

SupportNumerically

𝒙 −𝟐 −𝟏 𝟏 𝟐

𝒚−𝟐 𝟔𝟑

−𝟒𝟐𝟑

𝟒𝟐𝟑

𝟐 𝟔𝟑

(𝒙, 𝒚)

(−𝟐,−𝟐 𝟔𝟑) (−𝟏,−

𝟒𝟐𝟑) (𝟏,

𝟒𝟐𝟑) (𝟐,

𝟐 𝟔𝟑)

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Name:_________________________________________________Period:___________Date:________________

AnalyzingGraphsofFunctionsandRelationsAssignment

Copyright©PreCalculusCoach.com 12

Determinewhetherthefollowingareeven,odd,orneither.

SOLVEREALWORLDPROBLEM

13. 𝒇 𝒙 = 𝒙𝟑 + 𝟐𝒙

𝒇 𝒙 = 𝒙𝟑 + 𝟐𝒙𝒇 −𝒙 = −𝒙 𝟑 + 𝟐(−𝒙)𝒇 −𝒙 = −𝒙𝟑 − 𝟐𝒙𝒇 −𝒙 = −(𝒙𝟑 + 𝟐𝒙)𝒇 −𝒙 = −𝒇 𝒙 Thefunctionisodd.

14. 𝒈 𝒕 = 𝟐𝒕𝟒 + 𝒕𝟐

𝒈 𝒕 = 𝟐𝒕𝟒 + 𝒕𝟐𝒈 −𝒕 = 𝟐 −𝒕 𝟒 + −𝒕 𝟐𝒈 −𝒕 = 𝟐𝒕𝟒 + 𝒕𝟐𝒈 −𝒕 = 𝒈 𝒕 Thefunctioniseven.

15. 𝒉 𝒚 = 𝒚𝟒 − 𝟓𝒚𝟐 − 𝟑𝒚

𝒉 𝒚 = 𝒚𝟒 − 𝟓𝒚𝟐 − 𝟑𝒚𝒉 −𝒚 = −𝒚 𝟒 − 𝟓 −𝒚 𝟐 − 𝟑 −𝒚 𝒉 −𝒚 = 𝒚𝟒 − 𝟓𝒚𝟐 + 𝟑𝒚𝒉 −𝒚 ≠ 𝒉 𝒚 𝒉 −𝒚 ≠ −𝒉 𝒚 Thefunctionisneither

16. Thetemperature𝑻indegreesFahrenheit𝒕hoursafter6AMisgivenby𝑻 𝒕 = − 𝟏𝟐𝒕𝟐 − 𝟖𝒕 + 𝟑,

𝒇𝒐𝒓𝟎 < 𝒕 < 𝟏𝟎.Find𝑻 𝟎 ,𝑻 𝟐 and𝑻 𝟔 graphicallyandalgebraically.

Graphically

𝑻 𝟎 ≈ 𝟒𝑻 𝟐 ≈ −𝟏𝟏𝑻 𝟔 ≈ −𝟔𝟎

Algebraically

𝑻 𝟎 = −𝟏𝟐𝒕𝟐 − 𝟖𝒕 + 𝟑

𝑻 𝟎 = −𝟏𝟐∗ 𝟎 − 𝟖𝒕 ∗ 𝟎 + 𝟑 = 𝟑

𝑻 𝟎 = 𝟑

𝑻 𝟐 = −𝟏𝟐∗ 𝟐𝟐 − 𝟖 ∗ 𝟐 + 𝟑

𝑻 𝟐 = −𝟏𝟐∗ 𝟒 − 𝟏𝟔 + 𝟑

𝑻 𝟐 = −𝟐 − 𝟏𝟔 + 𝟑𝑻 𝟐 = −𝟏𝟓

𝑻 𝟔 = −𝟏𝟐𝟔𝟐 − 𝟖 ∗ 𝟔 + 𝟑

𝑻 𝟔 = −𝟏𝟐∗ 𝟑𝟔 − 𝟖 ∗ 𝟔 + 𝟑

𝑻 𝟔 = −𝟏𝟖 − 𝟒𝟖 + 𝟑𝑻 𝟔 = −𝟔𝟑

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