Name Rational Expressions and Functions 4.3 Mathematics Vision Project | MV P Licensed under the Creative Commons Attribution4NonCommercial4ShareAlike 3.0 Unported license 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). 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) ! ! − ! − 4 (! − 1) ! ! + 6! + 5 ! ! + 4! + 4 Simplify each expression (answers can be left in factored form). 10. !!!! !!! − ! (!!!) 11. !! !!! + !!! !!! 12. ! ! !!!!! ! ! !!!!! ∙ ! ! !!!!! ! ! !!!!! 13. ! ! !!!!! ! ! !!!!! ∙ ! ! !!!!! ! ! !!!!! 16

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Page 1: 16 Name%%%%%%%%%%%%%%%%%%%%%%Rational…

Name%%%%%%%%%%%%%%%%%%%%%%Rational%Expressions%and%Functions% 4.3$!

!Mathematics!Vision!Project!|!MVP!!!Licensed!under!the!Creative!Commons!Attribution4NonCommercial4ShareAlike!3.0!Unported!license!

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).!

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)!

!! − ! − 4(! − 1) !

!! + 6! + 5!! + 4! + 4!

Simplify!each!expression!(answers!can!be!left!in!factored!form).!!

10. !!!!!!! − !(!!!)!

11. !!!!! +!!!!!!!

!! !

12. !!!!!!!!!!!!!! ∙

!!!!!!!!!!!!!!!

13. !!!!!!!!!!!!!! ∙

!!!!!!!!!!!!!!!

Page 2: 16 Name%%%%%%%%%%%%%%%%%%%%%%Rational…

Name%%%%%%%%%%%%%%%%%%%%%%Rational%Expressions%and%Functions% 4.4#!

!Mathematics!Vision!Project!|!MVP!!!

Licensed!under!the!Creative!Commons!Attribution4NonCommercial4ShareAlike!3.0!Unported!license!

Ready,#Set,#Go!#

Ready#%

Topic:!Distinguishing!between!proper!and!improper!rational!functions.!

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!

! ! = !! − 5!! − 4! ! ! = !3!! − 2! + 7!! − 5 !

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!4.! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!5.!

!!!!!!!!!!!!!!!!!!!!!!!!!! ! = !!!!!!!!!!"!!! ! ! ! = 5!! − 4! + 4

7!! − 2! + 3!!

#6.!Which!of!the!above!functions!have!the!following!end!behavior:!!!

!"!! → ∞, ! ! → 0!!"#!!"!! → −∞, ! ! → 0!!

7.!Complete!the!statement:!ALL!proper!rational!functions!have!end!behavior!that!!!

________________________________________________________________________.!

#Set#Topic:!Features!of!rational!functions.!!

Find!the!xRintercept(s),!yRintercept,!roots,!asymptotes,!and!end!behavior!of!the!following!

functions.!

8.!!! ! = ! (!!!)(!!!)(!!!)(!!!)(!!!)! ! ! 9.!!! ! = ! (!!!!)

(!!!)(!!!)!!

Features!of!f(x):* * * * * Features!of!g(x):!

$7th Grade Math Chapter 3 Applying Rational Numberssmessy.weebly.com/uploads/3/8/9/7/38972613/7thgrademath-chapt… · 7th Grade Math Chapter 3 Applying Rational Numbers Name: _____$

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