Chp 3 Tutorial 3A BMQ Soln (RVHS)

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2022 Chp 3 Graphing Techniques (Part 1) (Solutions to Tutorial and Assignment) 1 Tutorial 3A: Graphing Techniques (Part 1) Curve Sketching, Conic Sections and Parametric Equations Basic Mastery Questions 1 (a) 3 1y x x   (b) 1 20y x  Lines of symmetry: ݕ= −ݔ+ 20, ݕ= ݔ− 20

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2022 Chp 3 Graphing Techniques (Part 1) (Solutions to Tutorial and Assignment) 2 (c) 20 1 4 xy x   Lines of symmetry: ݕ= ݔ+ 16, ݕ= −ݔ+ 24 (d) 2 2 3 5 7 10 x xy x x    

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2022 Chp 3 Graphing Techniques (Part 1) (Solutions to Tutorial and Assignment) 3 (e) 3 2e xy  (f) ln 2 3 xy     

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2022 Chp 3 Graphing Techniques (Part 1) (Solutions to Tutorial and Assignment) 4 (g) tan( )xy x Lines of Symmetry: x = 0 Note that there should be an open circle at (0, 1) Note that the pattern repeats infinitely many times in either direction. (h) 2e xy x  ݔ= 3ߨ 2

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2022 Chp 3 Graphing Techniques (Part 1) (Solutions to Tutorial and Assignment) 5 (i) lny x x Note that the graph is not defined for x = 0. 2 (a) 2 2 4x y  Lines of symmetry: y = mx for any real number m, x = 0

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2022 Chp 3 Graphing Techniques (Part 1) (Solutions to Tutorial and Assignment) 6 (b) 2 2( 2) 4 9x y   Lines of symmetry: y = 0, x = −2 (c) 2 2 4 4x y  Lines of Symmetry: x = 0, y = 0 ቆ0, √5 2 ቇ ቆ0, −√5 2 ቇ

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2022 Chp 3 Graphing Techniques (Part 1) (Solutions to Tutorial and Assignment) 7 (d) 2 2 2 29 y x x   Lines of Symmetry: x = 1, y = 0 3. (a) ݔ= 2ݐଶ,ݕ= −ݐ+ 1 →ݔ= 2(1 −ݕ)ଶ Lines of Symmetry: y = 1 Note, this is actually a parabola and is another type of conic. ݕଶ 3ଶ − (ݔ− 1)ଶ = 1

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2022 Chp 3 Graphing Techniques (Part 1) (Solutions to Tutorial and Assignment) 8 (b) ݔ= 1 −ݐଶ,ݕ= ݐ(1 −ݐଶ) →ݕ= ±ݔ√1 −ݔ Lines of Symmetry: y = 0 (c) ݔ= sin(ݐ), ݕ= 3 cos(ݐ)→ ݔଶ + ቀ ௬ ଷቁ ଶ = 1 Lines of Symmetry: x = 0, y = 0

H2 Mathematics (9758) JC1 River Valley High School, Mathematics Department, 2022 Chp 3 Graphing Techniques (Part 1) (Solutions to Tutorial and Assignment) 9 (d) ݔ= 2 sec(ݐ), ݕ= 3 tan(ݐ)→ 1 + ቀ ௬ ଷቁ ଶ = ቀ ௫ ଶቁ ଶ Lines of Symmetry: x = 0, y = 0