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Section 6.5 Operations with Functions
Algebra 2 Section 6.5 Operations with Functions
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Warm Up Simplify. Assume that all expressions are defined. #1 2π₯+5 β( π₯ 2 +3π₯β2) #2 (π₯β1) π₯+1 2 #3 π₯ 2 βπ₯β6 π₯ 2 β4
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Operations on functions is very much like operations on expressions.
Youβre creating a new function!
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Addition π+π π=π π +π(π) Example π π₯ =2 π₯ 2 β5π₯+11 π π₯ =5 π₯ 2 +2π₯β30
π+π π₯=2 π₯ 2 β5π₯+11+5 π₯ 2 +2π₯β30 π+π π₯=7 π₯ 2 β3π₯β19 Would π+π π₯ be a different function?
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Subtraction πβπ π=π π βπ(π) π π₯ =4π₯β2 π π₯ =6π₯+8 πβπ π₯= 4π₯β2 β 6π₯+8
πβπ π₯=4π₯β2β6π₯β8 πβπ π₯=β2π₯β10 Would πβπ π₯ be a different function?
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Try these Pg #2-4
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Multiplication ππ π=π(π)βπ(π) π π₯ =π₯β3 π π₯ =4π₯+2 ππ π₯= π₯β3 4π₯+2
ππ π₯= π₯β3 4π₯+2 ππ π₯= 4π₯ 2 +2π₯β12π₯β6 ππ π₯=4 π₯ 2 β10π₯β6 Would ππ π₯ be a different function?
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Division π π x= π(π) π(π) π(π)β π π π₯ = π₯ 2 +7π₯+12 π π₯ =π₯+3
π π π₯= π₯ 2 +7π₯+12 π₯+3 π π π₯= (π₯+4)(π₯+3) (π₯+3) π π π₯=π₯+4
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Same or Different? Would π π π₯ and π π π₯ be the same function?
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Try these! Pg. 446 #5-7
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Composition of functions
Composition of functions- this operation uses the output of one function as the input of another function πππ π=π π π This operation is NOT commutative!!! πππ π=π(π π )
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Start with the innermost parentheses 1st!
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Try These! Pg. 8-10
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Boots are 50% off Take an additional 40% off Are you getting 90% off
Boots are 50% off Take an additional 40% off Are you getting 90% off? When you get 40% off, what percent of the price are you paying?
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π π₯ =.50π₯ π π₯ =.40π₯ πππ π₯=π π π₯ π .50π₯ = π₯ What percent are you getting off of the original price?
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π π₯ = 2π₯ 2 π π₯ =π₯+2 Find πππ π₯= ? πππ π₯= ?
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Try these! Pg #11-14
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Homework/Classwork Pg #15-33 all, all
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