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# College Algebra MAC 1105C

University of Central Florida

GPA 3.95

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This 54 page Class Notes was uploaded by Priscilla Thiel IV on Thursday October 22, 2015. The Class Notes belongs to MAC 1105C at University of Central Florida taught by Staff in Fall. Since its upload, it has received 43 views. For similar materials see /class/227437/mac-1105c-university-of-central-florida in Calculus and Pre Calculus at University of Central Florida.

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Date Created: 10/22/15

100411 Lecture 7 28 32 MALL Hours 6 Starts 7 Opens Q2 7 Opens Test 2 Sched Opens at 103900 AM Prat Test2 All Pa O Choose the equation that best describes the graph 3 3 3 3 2 2 2 2 4 4 4 4 X X X X X X X X cl cl cl cl N mm 0 D A C Choose the correct graph ofthe equation fX 3 X 2 4 B D What is domain of fX X4 A 0094U400 B 0090U000 C 004U400 D 0090 E oo1 U 1 oo 1 What is domain of 9X j A 0094U400 B 0090U000 C 004U400 D 0090 E oo1 U 1 oo Function Operations Let fx and gx be functions For instance fx 2x1 gx 3x7 Then fx gx 2x13x7 5x8 Function Operations We do this sort of thing so often that we have the following shorthand f gX fx 90 f gX fx 90 ngX fx X 906 1 x go at o g 906 Function Operations Let fx and gx be functions For instance fx 2x1 gx 3x7 Then f gx 2x13x7 5x8 Function Operations Let fx and gx be functions For instance fx 2x1 gx 3x7 Then f gx 2x1 3x7 X 6 Function Operations Let fx and gx be functions For instance fx 2x1 gx 3x7 Then fgx 2x 13x 7 6xz17x7 Function Operations Let fx and gx be functions For instance fx 2x1 gx 3x7 Then x 2x1 3x7 Difference Quotient The difference quotient DQ for a function fx is defined as W 2 fx h fx Difference Quotient Let fx 962 Then what is f2 Difference Quotient Let fx 962 Then what is f2 22 4 Difference Quotient Let fx 962 Then what is fxh Difference Quotient Let fx x2 Then what is fxhxh2x22xhh2 Difference Quotient So then iffx x2 then fxhfx h DQ x22xhh2 x2 h 2xh Calculus Students THE DIFFERENCE QUOTIENT IS NOT THE DERIVATIVE Function Composition Let fx and gx be functions Then f 0 9X96 fgx is called functional composition Function Composition For instance fx 2x1 gx 3x7 f 0 9X36 fgx f3x 7 23x71 Function Operations ngX f 90906 is multiplication f 0 mm f 906 is composition Function Operations Let fx RINRIH 906 Then 2 MW f 20900 g Function Operations What s the domain Function Operations 2 1 x fogXX f 7 5 5 This isjust a line right So the domain is 00 00 Calculate fg0 What happens Function Operations To find the domain of fogx 1 Find the domain ofthe inner function g in this case and write this off to the side 2 Find the composition and simplify 3 Find the domain ofthe composition 4 Exclude from this domain any values that you excluded in 1 Quadratic Functions and Models A quadratic function will be written in one of two ways fx ax2 bxc standard form fx ax h2k vertex form Quadratic Functions and Models V Every quadratic function has a vertex at some hk This quadratic has its vertex at 25 In fact fx x 22 5 x72x7h soh2 Quadratic Functions and Models V Every quadratic function has a vertex at some hk This quadratic has its vertex at 25 In fact fx x 22 5 k5 sok5 Quadratic Functions and Models What ifl gave you the quadratic in 2 standard form though fx x2 4x 1 You have two options 1 Complete the square 2 Use the vertex formula Quadratic Functions and Models What ifl gave you the quadratic in 2 standard form though fx x2 4x 1 Vertex formula b 4 2 2a 2 1 How would we find k Quadratic Functions and Models Find hk the coordinates of the vertex for fx x2 10x 23 A 5 2 B 52 C 5 2 D 52 Quadratic Functions and Models The height of a toy rocket is given by ht 1612 3201 50 where t is the time in seconds after launch and h is measured in feet When does the rocket reach its maximum height Quadratic Functions and Models The height of a toy rocket is given by ht 16t2 320t 50 where t is the time in seconds after launch and h is measured in feet When does the rocket reach its maximum height A 10 seconds B 20 seconds C 10 seconds D 160 seconds Quadratic Functions and Models The height of a toy rocket is given by ht 16t2 320t 50 where t is the time in seconds after launch and h is measured in feet What is that maximum height h10 Synthetic Division Synthetic division is a shortcut method for performing long division It is used only when dividing by x k If we re dividing by x 3 what is k If we re dividing by x 5 what is k If we re dividing by x2 1 what is k Synthetic Division Let s say we wanted to calculate 2x2x1 x 3 x 3 2x2 x1 Synthetic Division Let s say we wanted to calculate 2x2x1 x 3 32 1 1 Synthetic Division Let s say we wanted to calculate 2x2x1 Synthetic Division 32 1 1 V 2 Synthetic Division 32 1 1 2 Synthetic Division 32 1 1 Synthetic Division 32 1 1 6 21 2 7 Synthetic Division 3 2 1 1 21 2 7 22 Synthetic Division 3 2 1 1 21 2 7 22 remainder Synthetic Division 32 1 1 6 21 2 7 22 2X2X1A 2 2x7 x 3 2 x 3 Synthetic Division 3 2 1 1 21 2 7 22 2x2x1x 32x722 Synthetic Division x4 1 What IS the remainder of x l A 0 B 2 C 1 D 1 Remainder Theorem Ifthe polynomial fx is divided by x k then the remainder is equal to fk Remainder Theorem Example fx 2x2x1 f323231183122 Polynomial Zeros A zero ofa polynomialfunction f is a number k such that fk 0 Sometimes called roots If k is a real number then this is an x intercept of the graph of fx Polynomial Zeros So for instance is 1 a zero ofx2 2x 1 f 1 122 1 1 0 So yes this is a zero Polynomial Zeros So for instance is 1 a zero ofx2 2x 1 We can also do this by synthetic division Expressf x in the form f x x kqx r for the given value of k 26 f 5I 3 22 3X1 k1 A fX X1 5X3 4x2 2x 1 2 B f X 1 5x3 4x2 2x 1 2 C x X1 5X36X2 4x 7 6 D f X 1 5x3 6X2 4x 7 6

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