Chp 3 Tutorial 3B APQ Soln (RVHS)

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2021 Chp 3 Graphing Techniques (Part 2) (Solutions to Tutorial and Assignment) 23 Additional Practice Questions Solutions 1. NYJC/2006/Promo/Q6 The diagram shows a sketch of  fy x . On separate diagrams, sketch the graphs of i)  fy x , [2]

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2021 Chp 3 Graphing Techniques (Part 2) (Solutions to Tutorial and Assignment) 24 ii)  f 1y x  , [3]

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2021 Chp 3 Graphing Techniques (Part 2) (Solutions to Tutorial and Assignment) 25 2. RJC/2006/Promo/Q2 The diagram below shows the graph of  fy x . The points A, B and C have coordinates 1( ,0)2 , (1, 2) and (3, 1) respectively. Sketch on separate diagrams, the graphs of (i) f 2 xy      , [1] x y  fy x C(3,1) B(1,2) 1 2( ,0)A  

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2021 Chp 3 Graphing Techniques (Part 2) (Solutions to Tutorial and Assignment) 26 (ii) f 12 xy      , [2] State, in each case, the coordinates of the points corresponding to A, B and C, where appropriate.

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2021 Chp 3 Graphing Techniques (Part 2) (Solutions to Tutorial and Assignment) 27 3. HCI/2006/Promo/Q6 The diagram below shows the graph of  f 1y x  . The curve has a maximum point at A 31, 2      , and axes intercepts at B(0, 1) and C(–1, 0). The lines 2x and 1y  are the asymptotes. Sketch the graphs of (a)   1 f 1y x  [3] x y B(0, 1) A C(–1, 0) x y (0, 1) ݔ= −1

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2021 Chp 3 Graphing Techniques (Part 2) (Solutions to Tutorial and Assignment) 28 (b)  fy x , [3] ݕ= f(1 −ݔ)→ f(1 +ݔ)→ f(ݔ) 4. SAJC/2006/Promo/Q9 (modified) a) The curve C has equation 2 3 x axy  where a is a constant. Given that C has a stationary point at x = 2, find the value of a and determine the nature of the stationary point. Write down the equation of the asymptotes of C. [4] ݕ= ௫యା௔ ௫మ =ݔ+ ܽݔିଶ ௗ௬ ௗ௫ = 1 − 2ܽݔିଷ = 0 when ݔ= 2 1 − ଶ ଼ܽ= 0 ܽ= 4 ௗమ௬ ௗ௫మ = 24ݔିସ > 0, therefore (2, 3) is a minimum point. Asymptotes: ݔ= 0 and ݕ= ݔ x y ൬0, 3 2൰ (1,1) ݔ= 3 (0, 2)

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2021 Chp 3 Graphing Techniques (Part 2) (Solutions to Tutorial and Assignment) 29 Hence sketch C, showing clearly the asymptotes and the coordinates of any point(s) of intersection with the coordinate axes. [2] b) The given diagram shows the graph of y = f(x). On separate di