Linear functions
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1 Sep 2303:21 p.m. Linear functions During this lesson we will : • Explore the equation of a straight line. • Discover algebraic relations between pairs of parallel and perpendicular lines. • Explore the absolute value function and its properties. • Recognise and draw piecewise linear functions.
Transcript of Linear functions
- 1. 1Sep2303:21p.m.Linear functionsDuringthislessonwewill: Exploretheequationofastraightline. Discoveralgebraicrelationsbetweenpairsofparallelandperpendicularlines. Exploretheabsolutevaluefunctionanditsproperties. Recogniseanddrawpiecewiselinearfunctions.
2. 2Sep2303:21p.m.Distance between two pointsAB 3. 3Sep2303:21p.m.The Midpoint formula:ABMx1 x2 4. 4Sep2303:21p.m.Linear functionsThe graph is a straight line. 5. 5Sep2303:21p.m.Gradient of a lineThe gradient of a line is a measure of its steepnessIfandpositive gradient negative gradient 6. 6Sep2303:21p.m.horizontal lines have a gradient of 0 (zero)vertical lines have an undefined gradientparallel lines have equal gradientsthe gradients of perpendicular lines arenegative reciprocalsif the gradients are m1 and m2 then:or 7. 7Sep2303:21p.m.Equations of linesThe equation of a line is an equation which states the connectionbetwen the xand y values for every point on the line.All vertical lines have equations of the form x=a, ( a is a constant)All horizontal lines have equations of the form y=c, ( c is a constant)slope-intercept form or explicit formgradienty-interceptgeneral form or implicit form(notafunction) 8. 8Sep2303:21p.m.Write down the gradient and y-intercept of these straightlines:y=5x22y=16x3x+2y8=0 9. 9Sep2303:21p.m.Sketch the graphs of these equations:y=2x1 3y+2x3=0 2yx+1=0 10. 10Sep2303:21p.m.Write down the equation of the straight line which passesthrough the points A (2,5) and B (6,17). 11. 11Sep2303:21p.m.Find the explicit and implicit equations of the linethrough (-1,3) with a slope of 5. 12. 12Sep2303:21p.m.Are L1 with equation 2xy+2=0 and L2 with equationx+4y1=0 perpendicular lines? 13. 13Sep2303:21p.m.Find the equation of the line through (1,-5) and (5,-2).Express the equation in the form Ax+By + C = 0, with A, B and Cinteger numbers. 14. 14Sep2303:21p.m.InterceptsxinterceptyinterceptxyThe x-intercept is found by letting y=0.The y-intercept is found by letting x=0. 15. 15Sep2303:21p.m.For the line with equation 2x - 3y =12, find axis intercepts. 16. 16Sep2303:21p.m.Find the point of intersection of the lines :3x+4y=29 and 2x5y=43x+4y=292x5y=4 17. 17Sep2303:21p.m.Attheendofthelesson:Reproduce exactly this drawing on your GDC. 18. 18Sep2303:21p.m.Attheendofthelesson:Reproduce exactly this drawing on your GDC. 19. 19Sep2303:21p.m.Can you give a formula for the followinggraph? 20. 20Sep2303:21p.m.Piecewise linear functionsDraw the graph of: 21. 21Sep2303:21p.m.Absolute valueExamples:1|6|=|3|= |27|= 22. 22Sep2303:21p.m.Equations: 23. 23Sep2303:21p.m.|x|3|x1|4In general: |x|aaxaa a0 24. 24Sep2303:21p.m.|x|>5|x2|4In general: |x|>axaa a0 25. 25Sep2303:21p.m.Absolute value function (Modulus)Sketch the graph of f(x). 26. 26Sep2303:21p.m. 27. 27Sep2303:21p.m.With calculator: Menu graphOPTNNum (F5)Abs (X)CasioTI-84 Y=MATH > 1 (X ) 28. AttachmentsY11Linearfunctions2010.odt
