3.6 interpreting functions - math with ms....
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SECONDARY MATH I // MODULE 3
FEATURES OF FUNCTIONS
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
3.6 Interpreting Functions A Practice Understanding Task
Giventhegraphoff(x),answerthefollowingquestions.Unlessotherwisespecified,restrictthedomainofthefunctiontowhatyouseeinthegraphbelow.Approximationsareappropriateanswers.
1. Whatisf(2)?
2. Forwhatvalues,ifany,doesf(x)=3?
3. Whatisthex-intercept?
4. Whatisthedomainoff(x)?
5. Onwhatintervalsisf(x)>0?
6. Onwhatintervalsisf(x)increasing?
7. Onwhatintervalsisf(x)decreasing?
8. Forwhatvalues,ifany,isf(x)>3?
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SECONDARY MATH I // MODULE 3
FEATURES OF FUNCTIONS
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
Considerthelineargraphoff(t)andthenonlineargraphofg(t)toanswerquestions9-14.Approximationsareappropriateanswers.
9. Whereisf(t)=g(t)?
10. Whereisf(t)>g(t)?
11. Whatisf(0)+g(0)?
12. Whatisf(-1)+g(-1)?
13. Whichisgreater:f(0)org(-3)?
14. Graph:f(t)+g(t)from[-1,3]
Thefollowingtableofvaluesrepresentstwocontinuousfunctions,f(x)andg(x).Usethetabletoanswerthefollowingquestions:
15. Whatisg(-3)?
16. Forwhatvalue(s)isf(x)=0?
17. Forwhatvaluesdoesf(x)seemtobeincreasing?
18. Onwhatintervalisg(x)>f(x)
19. Whichfunctionischangingfasterintheinterval[-5,-1]? Why?
x f(x) g(x)-5 44 -13-4 30 -9-3 20 -5-2 12 -1-1 6 30 2 71 0 112 0 153 2 194 6 235 12 276 20 31
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SECONDARY MATH I // MODULE 3
FEATURES OF FUNCTIONS
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
Usethefollowingrelationshipstoanswerthequestionsbelow.
ℎ ! = 2! ! ! = 3! − 2 ! ! = 8 ! = 4 ! = 5! + 1
20. Whichoftheaboverelationsarefunctions?Explain.
21. Findf(2),g(2),andh(2).
22. Writetheequationforg(x)+h(x).
23. Whereisg(x)<h(x)?
24. Whereisf(x)increasing?
25. Whichoftheabovefunctionshasthefastestgrowthrate?
Createagraphforeachofthefollowingfunctions,usingthegivenconditions
26. Thisfunctionhasthefollowingfeatures:f(2)ispositive;f(-2)=0,f(x)isalwaysIncreasingandhasadomainofAllRealNumbers.
27. Thisfunctionhasthefollowingfeatures:f(3)>f(6);f(1)=0;f(2)=4;f(x)isincreasingfrom[-5,3);hasadomainfrom[-5,10]
28. Thisfunctionhasthefollowingfeatures:f(x)hasaconstantrateofchange;f(5)=0
29. Createyourownconditions-haveatleastthreeandthencreateexampleswherethesolutioncouldbedifferentgraphs.
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