UNIT6. FUNCTIONS A. SERRA. 6.A Relations and functions. Class work Relations and functions: definition and examples. Testing for functions: the vertical.

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UNIT6. FUNCTIONS A. SERRA

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).

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.

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

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”)

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.

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.

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.

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

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

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

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

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).