S56 (5.1) Graphs of Functions.notebook September 22, 2016

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1 Daily Practice Q1. Write in completed square form y = 3x 2-18x + 4 Q2. State the equation of the line that passes through (2, 3) and is parallel to the x - axis Q1. If f(x) = 3x + k and g(x) = 5x - 1, find the value of k for which f(g(x)) = g(f(x)) Daily Practice Q3. Given f(x) = 2x 2 + 3x - 3 and g(x) = x + 2, find the f(g(x)) and state the nature of the roots of f(g(x)) Q2. Find the inverse of the function f(x) = 0.5(x + 1) Q3. The sequences defined by u n+1 = ku n + 2 and v n+1 = 0.5v n + 3 have the same limit. Find the value of k. Daily Practice Q1. A sequence is defined by u n+1 = mu n + 6 and term u 0 = 2, with -1 < m < 1. Find the value of m for which the sequence has a limit of 20. Today we will be completing a homework quiz. Q2. The functions f and g are defined on suitable domains by f(x) = and g(x) = 3x + 1. Find an expression for h(x) = f(g(x)) stating any restriction on the domain. Q3.Write 3x x + 2 in completed square form. Today we will be learning about graph transformations.

2 Transformations of Graphs: + a + a a> 0 a Graph shifts vertically upwards + a a< 0 Graph shifts vertically downwards a Transformations of Graphs: y = f(x + a) Graph shifts horizontally to the left y = f(x + a) a> 0 Transformations of Graphs: y =-f(x) y = -f(x) a y = f(x + a) a< 0 Graph shifts horizontally to the right a Reflect graph in x - axis Transformations of Graphs: y = kf(x) Transformations of Graphs: y =f(-x) y = f(-x) y = kf(x) Reflect graph in y - axis Stretch vertically by a factor of k if k> 1 Compress vertically by a factor of k if k< 1

3 Transformations of Graphs: y = f(kx) y = f(kx) Transformations of Graphs: Compress horizontally by a factor of k if k> 1 Stretch horizontally by a factor of k if 0< k < 1 Transformations of Graphs: 1. Daily Practice Q1. Given f(x) = 2x and g(x) = 3x 2-1,write an expression for f(g(x)) Draw a sketch of the curve y = -f(x - k), k>0 Q2. State the inverse of the function f(x) = -3x + 4 Q3. Given Un+1 = 0.5Un + 2, find the limit of the recurrence relation (Higher 2013 ammended) Q4. Write 2x 2-8x + 3 in the form p(x + a) 2 + b Transformations of Graphs: 2. Today we will be continuing to sketch the graphs of transformations. (Higher 2011 ammended) Draw a sketch of the curve y = f(x + 2) - 1

4 DailyPractice Transformations of Graphs: 3. (Higher 2006) Ex. 3P Q1, 2, 4, 5, 6, 8,11 Today we will be continuing to practise sketching graph transformations and learning about radians. Ex. 3P Q1, 2, 4, 5, 6, 8,11 Daily Practice

5 Radians A radian is the angle at the centre of a sector of a circle where the length of the arc is equal to the radius. Today we will be learning about radians and how to sketch trig. graph transformations. r 1 radian r r Arc Length = x 0 x πd 360 Radians To get an answer in radians on your calculator, just use RAD mode. Radians 1. Convert to radians To convert degrees to radians or radians to degrees, always remember = π radians 2. Convert 6π to degrees 5 3. Evaluate cos 4π 3 Ex. 4C Q1-4

6 daıly practıce c(6, 4) y = Sinx A(1, -2) y = Cosx y = Tanx The amplitude of a graph = (Distance between max. and min.) 2 The period of a graph is the length of the graph before it repeats itself. Period = b when y = asinbx 0 and y = acosbx 0 Period = b when y = atanbx 0 Advice: - Draw a new graph for each bit added to the function - Labels are expected. - Label roots and y - intercept. Reminder: Graph transformations

7 1. Sketch and annotate the graph of the function y = -2sinx Write a trigonometric function represented by the graph below that is in the form y = acos(x - b) 0 + k Daily Practice Today we will be continuing to practise drawing transformations of trig. graphs. 3. Sketch and annotate the graph of the function y = 2sin(x + ) 4. State the values of a, b and c for the graph of the function shown y = asin(bx) + c

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