TMJC H2 Chapter 2 Transformation of Curves Extra Practice Solutions

Chapter 2 Transformation of Curves TMJC 2024 Page 1 of 6 H2 Mathematics (9758) Chapter 2 Transformation of Curves Extra Practice Solutions Qn 1 2020/VJC/8b Before C, the equation of curve is 3 2 xy x +=− + Before B, the equation is 3 2 xy x += + Before A, the equation is ( 3) 3 ( 3) 2 1 xxy xx −+== − + − 1 xy x= − Qn 2 2020/CJC Prelim/1 (i) 23f( ) 35 21 3 3(3 5) 1 2 3 3 3 5 xx x x x += + =− + − =+ + (ii) y = 1 x → 1 1 1 99y xx ==  Step1: stretching by a factor of 1 9 parallel to the y-axis Or stretching by a factor of 1 9 parallel to the x-axis 1 9y x= → 1 59 3 y x =  + Step2: translation by 5 3 units in the negative x-direction 1 59 3 y x =  + → 1 59 3 y x =−  + Step3: reflection in the x-axis

Chapter 2 Transformation of Curves TMJC 2024 Page 2 of 6 1 59 3 y x =−  + → 21 53 9 3 y x =−  + Step4: translation by 2 3 units in the positive y-direction Qn 3 2020/RI Prelim/6 (a) (b) y ( ,0) x 0x=

Chapter 2 Transformation of Curves TMJC 2024 Page 3 of 6 Qn 4 2017/MI Promo/10 (modified) (i) (ii) (iii) (−1,8) (2,1) y x y = 5 − 2x y = |f(x)| O y = 2x − 5 x = 0 (−2,−1) (2,−1) y x y = 5 − 2x y = f(|x|) y = 2x + 5 x = 0 ൬−1, 1 8൰ (2,−1) y x y = 0 𝑦 = 1 fሺ𝑥ሻ (0,0)

Chapter 2 Transformation of Curves TMJC 2024 Page 4 of 6 Qn 5 2012/VJC Prelim/I/9(b) (modified) (i) ( )h3yx=+ (ii) ( )1 h2yx= (iii) ( )h3yx= − + 1 x y O 4 x y y = 0 O x = 0 x y y = 0 O Just replace by xx using original graph of ( )h3yx=− .

Chapter 2 Transformation of Curves TMJC 2024 Page 5 of 6 Qn 6 2017/RVHS Promo/6 (a) (i) (a) (ii) Note: 10, 8   is a sharp point. Qn 7 2018/MI Promo/2 y x y = 4 (0, 4) (2, 0) (−2, 0) x = −1 x = 4 y = f (x) y x (4,0) 0 (–4,0) ൬0, 1 8൰ y x O y = a (c, d) (0, b) (−k, 0)

Chapter 2 Transformation of Curves TMJC 2024 Page 6 of 6 Qn 8 2021/YIJC Prelim/2 (i) (ii) -4 2 y x O -3 4 -1 1 y x O -1 1