TJC 2025 IP4 Math Unit 16 Graphing with GC Lesson 3 (Student)

2025 Year 4 Math / Graphs Unit 16 Graphing with GC Page 1 Temasek Junior College (IP) 2025 Year 4 Mathematics Unit 16 – Graphing with Graphing Calculator (GC)1 Lesson 3: More Graphing, Graphical Solutions and Equation Solving on the GC Learning Objectives By the end of this lesson you should be able to: 1) Sketch the graphs of different functions with the aid of a graphing calculator (GC). 2) Solve equations using a GC. 3) Solve simple problems involving graphs using the GC. You may be asked to use a GC to aid you in graphing a variety of functions, both see n and unseen. As it is not possible to explore every type of function, you should learn to be competent in the use of the GC, such that you are ready to plot any function when required. In Lessons 1 and 2, we have attempted to plot some of the functions learned previously (polynomial, logarithmic, exponential, reciprocal, root etc) on the GC. In this lesson, we shall look at a few more. 3.1 Solving Inequalities using GC Sometimes we may be given questions that we are unable to solve easily using algebraic methods learnt so far. In this case, GC is able to help us visualize the problems and obtain the solutions. Example 1 (i) With the aid of a graphing calculator, sketch the graph of 32 2 5 5y x x x= + − − and 20.5 1y x x= + + , labeling coordinate of intersects and axial intercepts. (ii) Hence find the values of x that satisfies (a) 3 2 22 5 5 0.5 1x x x x x+ − − = + + , (b) 3 2 22 5 5 0.5 1x x x x x+ − −  + + . [Solution] 1 This set of notes is to be used in conjunction with the TI-84 Plus CE graphing calculator. Operation of other brands and models of graphing calculators may differ AM

2025 Year 4 Math / Graphs Unit 16 Graphing with GC Page 2 (i) The coordinates of the intersection points A, B and C are ( )2.86, 2.24− , ( )0.918,0.503− and ( )2.28,5.89 respectively. (ii) (a) The values of x that satisfy 3 2 22 5 5 0.5 1x x x x x+ − − = + + are the x- coordinates of the intersection points between the 2 graphs, 2.86x=− , 0.918x=− or 2.28x= . (b) The range of values of x that satisfy 3 2 22 5 5 0.5 1x x x x x+ − −  + + are the range of values of x when the y-coordinate of the cubic graph is greater than the y-coordinate of the quadratic graph. 2.86 0.918x−  − or 2.28x . y x 1 −5 −3.09 −0.837 1.93 A B C

2025 Year 4 Math / Graphs Unit 16 Graphing with GC Page 3 Exercise 1 With the aid of a graphing calculator, (a) sketch the graph of 2e1xy −=− and ( )3log 1yx=− . (b) solve ( ) 2 3e 1 log 1x x− − = − . [Solution] By zooming in closer to the region highlighted above, we see that there are two points of intersection instead of just one point of intersection. The coordinates of the intersection points between the graphs of 2e1xy −=− and 2e1xy −=− are ( )1.91, 0.0884− and ( )