Unit 2 Review: Polynomial Functions Name ! IcanidentifytheDomainofaFunctionusingintervalnotation 1. 𝑓 𝑥 = 2 4 − 𝑥 2. ℎ 𝑥 = !

! 3. 𝑔 𝑥 = 2𝑥! − 4𝑥 + 5

Domain:_____________ Domain:________________ Domain:_____________ ! Icanwriteapolynomialfunctionforagivengraph.[𝒇 𝒙 = 𝒂 𝒙 − 𝒓𝟏 𝒙 − 𝒓𝟐 . . . (𝒙 − 𝒓𝒏)] 4. Writeapolynomialfunctionforgivengraph.Findthevalueofa. ! Icandetermineifafunctioniseven/odd/neither[If𝒇 −𝒙 = 𝒇 𝒙 𝐄𝐕𝐄𝐍; 𝒇 −𝒙 = −𝒇 𝒙 𝐎𝐃𝐃] 5.𝑓 𝑥 = −2𝑥! − 𝑥________ 6. ℎ 𝑥 = !!

!________

! Icanfindtheinverseofafunction[Interchangex&yvariables,solvefory]

7.𝑓 𝑥 = 3 + 𝑥 − 2 ! 8. 𝑓 𝑥 = 41−3𝑥

𝑓!! 𝑥 =_______________________ 𝑓!! 𝑥 =________________________ ! Icanidentifytheend-behaviorofafunctionusingtheLeadingCoefficientTest.

Describetheend-behaviorofeachfunction. 9.𝑓 𝑥 = −4𝑥! + 𝑥! − 7𝑥 − 1 10.𝑓 𝑥 = 6𝑥4 − 𝑥3 + 5𝑥2 + 4 ! Icanwriteapolynomialfunctioninfactored&standardformforgivenzeros.

11. Findapolynomialfunctionwithzeros:4𝑖,−4𝑖, 0, 3where𝑓 2 = 28.

TheRemainderTheorem:Whenapolynomial𝑓(𝑥)isdividedby(𝑥 − 𝑘),theremainderis𝑓(𝑘).

TheRationalZeroTest:Thepossiblerationalzerosofapolynomial=± !"#$%&' !"#$%&' !"#$% !"#$%&#% !"#$

!"#$%$&' !"#$%&' !"#$% !"#$%&' !"#$$%!%#&'

! IcanapplytheRemainderTheoremtofindzerosofpolynomials 12. Findtheremainderwhen2𝑥! + 3𝑥! − 17𝑥 − 30isdividedbyeachofthefollowing: a) (𝑥 − 1)r=___________ b)(𝑥 + 2)r=___________ c) (𝑥 − 3) r=___________

! Icanusesyntheticdivisiontofindtheremainingzerosofafunction. 13.If𝑥 = 3isazeroof𝑓 𝑥 = 𝑥! + 16𝑥 − 8𝑥! − 3,usesyntheticdivisiontofindtheremainingzerosofthefunction.

Zeros:__________________________

! Icanuselongdivisiontodividepolynomialfunctions. 14.Divide:(6𝑥! − 2) ÷ (3𝑥 − 1)

! IcanusetheRationalZeroTesttofindpossiblezerosofapolynomial. 15.UsetheRationalZeroTesttofindthepossible rationalzerosof𝑓 𝑥 = 2𝑥! − 15𝑥! − 22𝑥 − 15. PossibleRationalZeros:____________________________________

! Icansolvepolynomialinequalities. 16.Solve:2𝑥! + 3𝑥 − 5 ≤ 0

! Icansolvewordproblemsinvolvingpolynomialfunctions. 17. Theprofitearnedbyacompanythatproduceshand-madesweaterscanbedescribedbythefunction 𝑃 𝑥 = 50𝑥 − 2000 − 0.02𝑥!dollarswherexisthenumberofsweatersproducedandsold.Howmany

sweatersshouldthecompanyproducetoreachthemaximumprofit?

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