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Www.projectmathsbooks.com Comparing, Shifting & Scaling Graphs.

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Presentation on theme: "Www.projectmathsbooks.com Comparing, Shifting & Scaling Graphs."— Presentation transcript:

1 www.projectmathsbooks.com Comparing, Shifting & Scaling Graphs

2 www.projectmathsbooks.com

3

4 Shifting and Scaling functions

5 www.projectmathsbooks.com -3 -2 0 1 2 3 -3 -2 0 1 2 3 -3 -2 0 1 2 3 -3 -2 0 1 2 3 -39(-3,9) -24(-2,4) 1(-1,1) 00(0,0) 11(1,1) 24(2,4) 39(3,9) -318(-3,18) -28(-2,8) 2(-1,2) 00(0,0) 12(1,2) 28(2,8) 318(3,18) -327(-3,27) -212(-2,12) 3(-1,3) 00(0,0) 13(1,3) 212(2,12) 327(3,27) -34.5(-3,4.5) -22(-2,2) 0.5(-1,0.5) 00(0,0) 10.5(1,0.5) 22(2,2) 34.5(3,4.5) -39(-3,9) -24(-2,4) 1(-1,1) 00(0,0) 11(1,1) 24(2,4) 39(3,9) -3 -2 0 1 2 3 31

6 www.projectmathsbooks.com -3 -2 0 1 2 3 -3 -2 0 1 2 3 -39(-3,9) -24(-2,4) 1(-1,1) 00(0,0) 11(1,1) 24(2,4) 39(3,9) -3-9(-3,-9) -2-4(-2,-4) (-1,-1) 00(0,0) 1(1,-1) 2-4(2,-4) 3-9(3,-9) -3-27(-3,-27) -2-12(-2,-12) -3(-1,-3) 00(0,0) 1-3(1,-3) 2-12(2,-12) 3-27(3,-27) -3-4-5(-3,-4.5) -2 (-2,-2) -0.5(-1,-0.5) 00(0,0) 1-0.5(1,-0.5) 2-2(2,-2) 3-4.5(3,-4.5) -39(-3,9) -24(-2,4) 1(-1,1) 00(0,0) 11(1,1) 24(2,4) 39(3,9) -3 -2 0 1 2 3 31

7 www.projectmathsbooks.com -3 -2 0 1 2 3 -3 -2 0 1 2 3 -312(-3,12) -27(-2,7) 4(-1,4) 03(0,3) 14(1,4) 27(2,7) 312(3,12) -35(-3,5) -20(-2,0) -3(-1,-3) 0-4(0,-4) 1-3(1,-3) 20(2,0) 35(3,5) -39(-3,9) -24(-2,4) 1(-1,1) 00(0,0) 11(1,1) 24(2,4) 39(3,9) -310(-3,10) -25(-2,5) 2(-1,2) 01(0,1) 12(1,2) 25(2,5) 310(3,10) -39(-3,9) -24(-2,4) 1(-1,1) 00(0,0) 11(1,1) 24(2,4) 39(3,9) -3 -2 0 1 2 3 32

8 www.projectmathsbooks.com -3 -2 0 1 2 3 -3 -2 0 1 2 3 -3-6(-3,-6) -2(-2,-1) 2(-1,2) 03(0,3) 12(1,2) 2(2,-1) 3-6(3,-6) -3-13(-3,-13) -2-8(-2,-8) --5(-1,-5) 0-4(0,-4) 1-5(1,-5) 2-8(2,-8) 3-13(3,-13) -39(-3,9) -24(-2,4) 1(-1,1) 00(0,0) 11(1,1) 24(2,4) 39(3,9) -3-8(-3,-8) -2-3(-2,-3) 0(-1,0) 01(0,1) 10(1,0) 2-3(2,-3) 3-8(3,-8) -39(-3,9) -24(-2,4) 1(-1,1) 00(0,0) 11(1,1) 24(2,4) 39(3,9) -3 -2 0 1 2 3 32

9 www.projectmathsbooks.com -39(-3,9) -24(-2,4) 1(-1,1) 00(0,0) 11(1,1) 24(2,4) 39(3,9) -4 -3 -2 0 1 2 -39(-3,9) -24(-2,4) 1(-1,1) 00(0,0) 11(1,1) 24(2,4) 39(3,9) -49(-4,9) -34(-3,4) -21(-2,1) 0(-1.0) 01(0,1) 14(1,4) 29(2,9) -6 -5 -4 -3 -2 0 -3 -2 0 1 2 3 -60(-6,9) -51(-5,4) -44(-4,1) -39(-3,0) -216(-2,1) 25(-1,4) 036(0,9) -36.25(-3,6.25) -22.25(-2,2.25) 0.25(-1,0.25) 00.25(0,0.25) 12.25(1,2.25) 26.25(2,6.25) 312.25(3,12.25) 33

10 www.projectmathsbooks.com -39(-3,9) -24(-2,4) 1(-1,1) 00(0,0) 11(1,1) 24(2,4) 39(3,9) -2 0 1 2 3 4 -39(-3,9) -24(-2,4) 1(-1,1) 00(0,0) 11(1,1) 24(2,4) 39(3,9) -29(-3,9) 4(-2,4) 01(-1,1) 10(0,0) 21(1,1) 34(2,4) 49(3,9) 0 2 3 4 5 6 -3 -2 0 1 2 3 09(0,9) 14(1,4) 21(2,1) 30(3,0) 41(4,1) 54(5,4) 69(6,9) -312.25(-3,12.25) -26.25(-2,6.25) 2.25(-1,2.25) 00.25(0,0.25) 10.25(1,0.25) 22.25(2,2.25) 36.25(3,6.25) 33

11 www.projectmathsbooks.com -39(-3,9) -24(-2,4) 1(-1,1) 00(0,0) 11(1,1) 24(2,4) 39(3,9) -4 -3 -2 0 1 2 -39(-3,9) -24(-2,4) 1(-1,1) 00(0,0) 11(1,1) 24(2,4) 39(3,9) -49(-4,9) -34(-3,4) -21(-2,1) 0(-1,0) 01(0,1) 14(1,4) 29(2,9) -4 -3 -2 0 1 2 -4 -3 -2 0 1 2 -411(-4,11) -36(-3,6) -23(-2,3) 2(-1,2) 03(0,3) 16(1,6) 211(2,11) -4 -3 -2 0 1 2 34 -411(-4,11) -36(-3,6) -23(-2,3) 2(-1,2) 03(0,3) 16(1,6) 211(2,11) -47(-4,7) -32(-3,2) -2(-2,-1) -2(-1,-2) 0(0,-1) 12(1,2) 27(2,7)

12 www.projectmathsbooks.com GraphFunction Local Maximum/Minimum 1 2 3 4 5 6 7 8 9 10 Activity 2 GraphFunction Local Maximum/Minimum 1 Local min (0,0) 2 3 Local max(0,0) 4 Local min (0,3) 5 Local min (0,-1) 6 Local max (0,-1) 7 Local max (0,3) 8 Local min (-1,0) 9 Local min (3,0) 10 Local min (-1,2) 35

13 www.projectmathsbooks.com GraphFunction Local Maximum/Minimum 1 11 12 13 14 15 16 17 18 19 20 Activity 2 GraphFunction Local Maximum/Minimum 1 11Local min (0,1) 12Local min (0,0) 13Local min (2,0) 14Local max (0,0) 15Local max (0,-1) 16Local min (-3,-2) 17Local min (2,3) 18 19 20 35

14 www.projectmathsbooks.com GraphFunction Local Maximum/Minimum 1 11 12 13 14 15 16 17 18 19 20 Activity 2 GraphFunction Local Maximum/Minimum 1 11Local min (0,1) 12Local min (0,0) 13Local min (2,0) 14Local max (0,0) 15Local max (0,2) 16Local min (-3,-2) 17Local min (2,3) 18Local max (0,-1) 19Local max (1,2) 20Local max (-3,4) 35

15 www.projectmathsbooks.com GraphFunction Local Maximum/Minimum 21 22 23 24 GraphFunction Local Maximum/Minimum 21 22 23 24 f(x) =sin(x)+5 Activity 2 35

16 www.projectmathsbooks.com Which is the best format? Can we change from one format to the other and back again? Activity 3 36

17 www.projectmathsbooks.com Activity 3 -2 0 1 2 3 4 5 6 -2 0 1 2 3 4 5 6 -2 0 1 2 3 4 5 6 -27(-2,7) 0(-1,0) 0-5(-1,5) 1-8(1,-8) 2-9(2,9) 3-8(3,-8) 4-5(4,-5) 50(5,0) 67(6,7) -27(-2,7) 0(-1,0) 0-5(-1,5) 1-8(1,-8) 2-9(2,9) 3-8(3,-8) 4-5(4,-5) 50(5,0) 67(6,7) -27(-2,7) 0(-1,0) 0-5(-1,5) 1-8(1,-8) 2-9(2,9) 3-8(3,-8) 4-5(4,-5) 50(5,0) 67(6,7) 4. What items of information from each of the functions can help us if sketching the graph of a function? 36

18 www.projectmathsbooks.com Activity 4 Graph Matching

19 www.projectmathsbooks.com FSCSTPIRG Local max at (4,4) Local min at (5,-1) Local min at (-3,-1) Local min at (1,-9) Local min at (3,0) Local max at (1,4) Graph Matching Activity 4 Solutions FSCSTPIRG F4S6V2TP1Y4R3G6 F6S4V1TP2Y6R4G5 F2S2V5TP4Y2R6G4 F5S5V3TP3Y3R2G1 F1S3V6TP6Y1R5G2 F3S1V4TP1Y5R1G3

20 www.projectmathsbooks.com FSCSTPIRG Local min at (1,-9) Local min at (3,0) Local max at (1,4) Local min at (-3,-1) Local min at (5,-1) Local max at (4,4) Graph Matching Activity 4 Solutions FSCSTPIRG F5S5V3TP3Y3R2G1 F1S3V6TP6Y1R5G2 F3S1V4TP1Y5R1G3 F2S2V5TP4Y2R6G4 F6S4V1TP2Y6R4G5 F4S6V2TP1Y4R3G6

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