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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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x
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-4 -3 -2 -1 1 2 3 4
-4
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-2
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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
y
-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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-4 -3 -2 -1 1 2 3 4
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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
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3
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x
y
-4 -3 -2 -1 1 2 3 4
-4
-3
-2
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x
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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
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-2
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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
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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
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50
60
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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
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-4 -3 -2 -1 1 2 3 4
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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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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
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-4 -3 -2 -1 1 2 3 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
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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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