TMJC H2 Chapter 2 Transformation of Curves Discussion Questions (Suggested Solutions)

Chapter 2 Transformations of Curves TMJC 2024 Page 1 of 14 H2 Mathematics (9758) Chapter 2 Transformations of Curves Discussion Questions (Suggested Solutions) Level 1 1 Describe a single transformation that will change ( )fyx= into each of the following functions in part (a) – (f). The diagram shows the graph of ( )fyx= . On separate diagrams, sketch the graphs of the following, showing clearly the coordinates of intersection with the axes. (a) ( )f1yx=− (b) ( )f2yx=− (c) ( )2fyx= (d) f 3 xy =  (e) ( )fyx=− (f) ( )fyx=− (g) ( )fyx= O y x 1 3 (–2, –1) (2, –1) 2

Chapter 2 Transformations of Curves TMJC 2024 Page 2 of 14 1 Solution (a) ( )f1yx=− Transformation: Translation of 1 unit in the negative y-direction. (b) ( )f2yx=− Transformation: Translation of 2 units in the positive x-direction. (c) ( )2fyx= Transformation: Stretch of factor 2 parallel to the y-axis. (d) f 3 xy =  Transformation: Stretch of factor 3 parallel to the x-axis. O y x (–2, –2) (2, –2) (0,1) (2, 2) O (0, –1) (4, –1) y x (3,0) (5,0) O y x (1,0) (3,0) (–2, –2) (2, –2) (0,4) O y x (3,0) (9,0) (–6, –1) (6, –1) (0,2) Replace x by x − 2 x-coordinates increases by 2, y-coordinates remain unchanged Replace y by 2 y x-coordinates remain unchanged, y-coordinates multiplied by 2 Replace y by y + 1 x-coordinates remain unchanged, y-coordinates decreases by 1 Replace x by 3 x x-coordinates multiplied by 3, y-coordinates remain unchanged

Chapter 2 Transformations of Curves TMJC 2024 Page 3 of 14 (e) ( )fyx=− Transformation: Reflection in the x-axis. (f) ( )fyx=− Transformation: Reflection in the y-axis. (f) ( )fyx= O y x (1,0) (3,0) (–2, –1) (2, –1) (0,2) Replace x by x− x-coordinates multiplied by 1− , y-coordinates remain unchanged Replace y by y− x-coordinates remain unchanged, y-coordinates multiplied by 1− y x (–3,0) (–1,0) (1,0) (3,0) O (–2, 1) (2, 1) (0,–2) y x (–3,0) (1,0) (3,0) O (–2, 1) (2, 1) (0,2) (–1,0)

Chapter 2 Transformations of Curves TMJC 2024 Page 4 of 14 Level 2 2 The diagram shows the graph of ( )fyx= with asymptotes 0x= and yx= . The points A, B, O have coordinates ( )1, 2−− , ( )1, 2 , ( )0, 0 respectively. Sketch on separate diagrams the graph of (i) 13f 2yx =  , (ii) ( )2f 4yx=+ , (iii ) ( )f 2 1yx=+ , showing in each case the coordinates of the points corresponding to A, B and O and the equations of the asymptotes where applicable. 2 Suggested Solutions (i) 3f 2 xy =  (ii) ( )2f 4yx=+ (iii) ( )f 2 1yx=+ Note: For (ii), y-intercept of asymptote y = 2x +8 is (0, 8) and should be higher than turning point (3, −4) in your sketch