Name%%%%%%%%%%%%%%%%%%%%%%Rational%Expressions%and%Functions% 4.3$!
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Set$!
Answer!the!following!questions!to!gain!a!deeper!understanding!of!rational!expressions.!
7. Define!rational!expression!and!give!three!examples!(two!proper,!one!improper).!
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8. Circle!the!expressions!below!that!are!rational.!
!!!!!!!!! ! !
!!!!"!!! ! !!"# !!!!! ! !!!!!!!!!!!!!!
!!!!!!!!!!!!!! ! ! + 3! ! !!!!!!!
! !
!
9. Angela!simplified!the!following!rational!expressions.!She!correctly!simplified!one!out!of!the!three!problems.!Determine!which!one!she!answered!correctly.!Also,!identify!and!correct!where!she!went!wrong!in!the!other!two!problems.!!
a.!!!!!!!!!!!!!! !!!!! + !
(!!!)!!
b.!!!!!!!!!!!!! !!!! − !(!!!)
(!!!) ! c.!!!(!!!)(!!!)(!!!) × (!!!)(!!!)(!!!)!
5!(! − 1)! − 3 (! − 1) +
2(! − 3)(! − 3)(! − 1)!
!
!1 −
4(! − 1)!
(! + 1)(! − 2)(! + 5)(! + 2)(! − 2)(! + 2)!
5!! − ! + 2! − 6! − 3 (! − 1) !
!
!(! − 1)(! − 1) −
4(! − 1)!
(! + 1)(! + 5)(! + 2)(! + 2)!
5!! + ! − 6! − 3 (! − 1)!
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!! − ! − 4(! − 1) !
!! + 6! + 5!! + 4! + 4!
Simplify!each!expression!(answers!can!be!left!in!factored!form).!!
10. !!!!!!! − !(!!!)!
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11. !!!!! +!!!!!!!
!! !
12. !!!!!!!!!!!!!! ∙
!!!!!!!!!!!!!!!
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13. !!!!!!!!!!!!!! ∙
!!!!!!!!!!!!!!!
!!
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Name%%%%%%%%%%%%%%%%%%%%%%Rational%Expressions%and%Functions% 4.4#!
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!Mathematics!Vision!Project!|!MVP!!!
Licensed!under!the!Creative!Commons!Attribution4NonCommercial4ShareAlike!3.0!Unported!license!
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Ready,#Set,#Go!#
Ready#%
Topic:!Distinguishing!between!proper!and!improper!rational!functions.!
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Determine!if!each!of!the!following!is!a!proper!or!an!improper!rational!function.!!
(Hint:!look!at!the!degree!of!the!polynomials.)!
1.! 2.! 3.!
! ! = !! + 3!! + 77!! − 2! + 1!
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! ! = !! − 5!! − 4! ! ! = !3!! − 2! + 7!! − 5 !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!4.! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!5.!
!!!!!!!!!!!!!!!!!!!!!!!!!! ! = !!!!!!!!!!"!!! ! ! ! = 5!! − 4! + 4
7!! − 2! + 3!!
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#6.!Which!of!the!above!functions!have!the!following!end!behavior:!!!
!"!! → ∞, ! ! → 0!!"#!!"!! → −∞, ! ! → 0!!
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7.!Complete!the!statement:!ALL!proper!rational!functions!have!end!behavior!that!!!
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#Set#Topic:!Features!of!rational!functions.!!
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Find!the!xRintercept(s),!yRintercept,!roots,!asymptotes,!and!end!behavior!of!the!following!
functions.!
8.!!! ! = ! (!!!)(!!!)(!!!)(!!!)(!!!)! ! ! 9.!!! ! = ! (!!!!)
(!!!)(!!!)!!
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Features!of!f(x):* * * * * Features!of!g(x):!
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