TJC 2025 IP4 Mathematics Structured Remedial Term 2 Session 3 - Graphing Without GC Cubic_Reciprocal

Temasek Junior College (IP) 2025 Year 4 Mathematics Structured Remedial Term 2 Session 3 – Graphing Without GC (Cubic and Reciprocal Graphs) Questions 1 (i) Sketch the graph of 2 1 1y x=− , stating the coordinates of all the intersections with the axes and the equations of all the asymptotes. (ii) By adding a suitable line to your graph , determine the number of solutions to the equation 22 3xxx =+ , showing your working clearly. [2020/TJC/IP4/AM/WA1/Q4] 2 (i) Find the values of x that satisfies 3 4xx= . (ii) On the same set of axes, sketch the graphs of 4yx= and 3yx= , labelling coordinates of intersection points, intersection with the axes. (iii) Hence, state the range of values of x which satisfies 3 4xx . [2021/TJC/IP4/IM/WA1/Q4] 3 (i) Sketch the graph of 2 1y x= − , labelling the intersections with the axes and the asymptotes clearly. (ii) By adding a suitable graph to part (a)(i), find the range of values of x where 2 11x − . [2019/TJC/IP4/IM/WA1/Q2(a)]

Answers 1. (ii) Sketch the line 11 22yx=+ . Number of solutions to the equation is 3. 2 (i) 0x= or 2x=− or 2x= (ii) (iii) 20 x−   or 2x

3 (i) (ii) Sketch 1y= 13 x y x x = 1 y = 0 y = 1 1 −2 (3, 1)