Chp 3 Tutorial 3B BMQ Soln (RVHS)

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2021 Chp 3 Graphing Techniques (Part 2) (Solutions to Tutorial and Assignment) 1 Tutorial 3B: Graphing Techniques (Part 2) Transformation of Graphs Basic Mastery Question 1. The diagram shows the graph of y = f(x), where f(x) =  20x x  . The points A, B and C have coordinates (0,0) , (10, 100) and (20,0) respectively. For each of the following transformations of this function: (i) describe the transformation(s) geometrically; (ii) write down an expression for the new function; (iii) sketch the graph of the transformed function, indicating the coordinates of the points corresponding to points A, B and C. (a) y = f(x) + 20 1. (a) (i) Translation of 20 units in positive y-direction (ii) ݕ= ݔ(ݔ− 20) + 20 10 20 30 –100 100 x y B A C

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2021 Chp 3 Graphing Techniques (Part 2) (Solutions to Tutorial and Assignment) 2 (iii) (b) y = f(x – 10) (b) (i) Translation of 10 units in the positive x-direction (ii) ݕ= (ݔ− 10)(ݔ− 30) (iii) (c) y = f(2x) (c) (i) Scaling by factor ½ parallel to the x-axis.

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2021 Chp 3 Graphing Techniques (Part 2) (Solutions to Tutorial and Assignment) 3 (ii) ݕ= 4ݔ(ݔ− 10) (iii) (d) y = 5f(x) (d) (i) Scaling by factor 5 parallel to the y-axis (ii) ݕ= 5ݔ(ݔ− 20) (iii) (e) y = 3f(x) (e) (i) Scaling by factor 3 parallel to the y-axis, and reflection about the x-axis. (ii) ݕ= −3ݔ(ݔ− 20)

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2021 Chp 3 Graphing Techniques (Part 2) (Solutions to Tutorial and Assignment) 4 (iii) (f) y = f( x) (f) (i) Scaling by factor 3 parallel to the x-axis, and reflection about the y-axis. (ii) ݕ= ଵ ଽݔ(ݔ+ 60) (iii) 2. The diagram shows the graph of y = f(x). Possible equation: ݂(ݔ)= ቐ − ଶ௫ ௫ିଶ if ݔ< 2 ି௫మାଷ௫ିଷ ௫ିଶ if ݔ> 2 1 3 0 y x 2 -2 (3,– 3)

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2021 Chp 3 Graphing Techniques (Part 2) (Solutions to Tutorial and Assignment) 5 Sketch on separate diagrams, the graphs of (a) 4 f( 1)y x   (b) 2f( ) 4y x  (c) f (2 1)y x 

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2021 Chp 3 Graphing Techniques (Part 2) (Solutions to Tutorial and Assignment) 6 Your diagrams should indicate the asymptotes and coordinates of the maximum point.

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2021 Chp 3 Graphing Techniques (Part 2) (Solutions to Tutorial and Assignment) 7 3. The diagram shows the graph of f ( )y x . ݈ܾ݁݅ݏݏ݋ܲ ݊݋݅ݐܽݑݍܧ:ݕ = ⎩ ⎪ ⎨ ⎪ ⎧ 1 ݔ+ 1 if ݔ< −1 ݔ ݔଶ − 1 if |ݔ| < 1 1 ݔ− 1 if ݔ> 1 On separate diagrams, sketch the graph of (i) | f ( ) |y x x y 1 1 0 y x

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2021 Chp 3 Graphing Techniques (Part 2) (Solutions to Tutorial and Assignment) 8 (ii) f ( )y x (iii) 1 f ( )y x Note the original graph doesn’t have sufficient information to deduce the existence of an oblique asymptote. It is sufficient to show the curve tending towards infinity.