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UNIT6. FUNCTIONS A. SERRA

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6.A Relations and functions. Class work Relations and functions: definition and examples. Testing for functions: the vertical line test. Graphical notes: open circle, filled-in circle, arrow head. Function notation: function f: such that x is converted into 2x+3 or f(x)=2x+3 Domain and Range. Examples Reminder : Title > Theory >Examples (if necessary) > Exercises> Correct ( ✓, ✗,?) 20% hwk> Extra (even + PS + HL) Individual work: 1.Watch videos “Introduction to functions” and/or “Relations and functions” 2.Examples H&H 1A, 1B & 1C 3.H&H 1A:2,4 (page 19). 4.H&H 1B:1 (only 3 letters) (page 21). 5.H&H 1C:2,4 (page 23).

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6.B. Composite Functions. Class work: Composite function f o g = f(g(x)). Examples f(g(x)) = g(f(x)) ???? Individual work: 1.Watch video “composite functions”. 2.Examples H&H 1D 3.H&H 1D:1, 3 (page 27). Small group work (groups of 3/4):. Investigation on page 25 (H&H). Possible video presentation: use Wolfram interactive demonstration to prove your results.

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6.C. The reciprocal function / Inverse functions / Identity function. Class work: Reciprocal function: f(x)= 1/x, using GDC to graph. Symmetry and Asymptotes; Inverse functions: e.g. y=5x+2 >> x = (y-2)/5 Identity function: e(x) = x Individual work: 1.Examples H&H 1E, 1F.and 5F 2.Exercise H&H 1E :1 3.Exercise H&H 1F: 3 and 7 4.Exercise H&H 1G: 3 5.Exercise H&H 5F: 3

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6.D. Families of Functions. Class work: Using GDC and/or GeoGebra to graph functions. Types of functions: linear, quadratic, cubic, absolute value, reciprocal, exponential, logarithmic, circular (trigonometric). Small group work (groups of 3/4):. Investigation “Function Families” H&H Page 120. Possible video presentation: use GeoGebra interactive demonstration to prove your results. Individual work: 1.H&H Examples 6A (page 121) 2.H&H 6A: 1,2,3,4,5,6 (only letter “a”)

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6.E. kEy fEatures of functions. Class work: Using GDC to graph functions. Types of keys: x-axis intercept, y-axis intercept, slope, vertex, turning points (maximum, minimum), asymptotes, limits, period, amplitude. Small group work (groups of 3/4):. Investigation “Key features of Functions” H&H Exercise 6B Pages 122-123. NB. You need to draw sketches of all the graphs from your GDC. Possible video presentation: use a GeoGebra interactive demonstration to prove your results. Individual work: You need to finish the investigation above. You might want to do a presentation on your own. Exercise 13D2:3 (page 275). Write conclusions (theory) of all exercises in your notebook.

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6.F. TransFormations of Functions. Class work: Using GDC and/or GeoGebra to graph functions (reloaded). Types of transformations: translation (vertically/horizontally), stretch (vertically/horizontally), reflection (in the x-axis/y-axis). Small group work (groups of 3/4):. Investigation “Transformations of functions” H&H 6C1:2,4 ; 6C2:2,4 ; 6C3 Pages 123-125. NB. You need to draw sketches of all the graphs from your GDC. Possible video presentation: use a GeoGebra interactive demonstration to prove your results. Individual work: You need to finish the investigation above. You might want to do a presentation on your own. Exercise 13D2:5 (page 275) Write conclusions (theory) of all exercises in your notebook.

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6.G.Transformations of Graphs. Class work: Review types of transformations: translation (vertically/horizontally), stretch (vertically/horizontally), reflection (in the x-axis/y-axis). Now with graphs… Small group work (groups of 3/4):. Investigation “Transformations of graphs” H&H 6D Pages 126-127. NB. You need to draw sketches of all the graphs from your GDC. Possible video presentation: use a GeoGebra interactive demonstration to prove your results. Individual work: You need to finish the investigation above. You might want to do a presentation on your own. Write conclusions (theory) of all exercises in your notebook.

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6.H.Solving Quadratic Equations. Class work: Review quadratic equations: factorisation, completing the square, quadratic formula.Examples Now using GDC… Individual work: Examples 8D, 8E Pages 163-173. Compulsory if you “forgot”. H&H 8D1:1; 8D2:2; 8E:1; 8F:1 (sketch graphs); 8G:5,7, 9 Extra (HL) 8G:11

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6.I Graphs of Quadratic Functions. Class work: Pre-loaded GeoGebra demonstrations: functions-quadratic Small group work (groups of 3/4):. Investigation “Graphs of Quadratic Equations (1,2,3)”. See website and H&H Page 155. NB. You need to draw sketches of all the graphs from your GDC/GeoGebra. Possible video presentation of ONE investigation: use a GeoGebra interactive demonstration to prove your results. Individual work: You need to finish the investigations above. You might want to do a presentation on your own. Write conclusions (theory) of all exercises in your notebook. Check H&H pages 156,175, 180 and 181. Exercise H&H 8B1:2, 8B2:2

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6.J Graphs of Exponential and Logarithmic Functions. Class work: Pre-loaded GeoGebra demonstrations: functions-exponential & Logarithmic Small group work (groups of 3/4):. Investigation “Graphs of Exponential Functions”. See website and H&H Page 76. NB. You need to draw sketches of all the graphs from your GDC/Geogebra. Possible video presentation of ONE investigation: use a GeoGebra interactive demonstration to prove your results. Individual work: You need to finish the investigations above. You might want to do a presentation on your own. Write conclusions (theory) of all exercises in your notebook. Check H&H page 77. Exercise H&H 3G: 2,3

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6.K Graphs of Trigonometric Functions. Class work: Pre-loaded GeoGebra demonstrations: functions-trigonometric Small group work (groups of 3/4):. Investigation “Graphs of Trigonometric Functions”. See website and H&H Page 271,273. NB. You need to draw sketches of all the graphs from your GDC/Geogebra. Possible video presentation of ONE investigation: use a GeoGebra interactive demonstration to prove your results. Individual work: You need to finish the investigations above. You might want to do a presentation on your own. Write conclusions (theory) of all exercises in your notebook. Check H&H page 274. Exercise H&H 13D2:1

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6.L Finding a function given its graph. Class work: And now….. Backwards! Examples and introduction to Task2 (See Portfolio) Individual work: Example pages 182-184,276-277 Exercise H&H 8J:1,2,3,4. Remember that you can do only 3 letters if you find it easy. Exercise H&H 13E: 2,5 Extra: Real life Investigation H&H 13E:4 (easy but long).

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Review unit 6 INDIVIDUAL WORK HOMEWORK Check Answers and Method of all exercises listed pages in this presentation. Review Set 1A (H&H). Review set 6 Do them, correct your answers and write down score (total and percentage “%” Online Quizzes: Ibmaths.com & MyiMaths.com Extra: Other Review Sets (Do, correct your answers and write down score (total and percentage “%”. Label it as “extra” in your notebook) Extra: Create an online quiz using Google forms and share it with the group. Please make sure your answers are correct. If you do this task you should add it to your online portfolio and submit it. Next> Mock TEST Unit 6

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Assessment unit 6 This unit will be assessed: Mini-quizzes. 5% Presentation(s) 10% Group Quiz 5% Test 1 40% Test 2 40%

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