TJC 2025 IP4 Math Unit 16 Graphing with GC Lesson 2 (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 2: Analysing Graphical Behaviour 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) Analyse behaviour of the graphs of different functions with the aid of a GC. 3) Solve simple problems involving graphs using the GC. 2.1 Asymptotic Behaviour Consider graphing the function 1 11y x=+ − using the GC. Recall: • The Y= button will bring you to the graphing interface. • To enter fractions use ALPHA Y= 1. • To enter the variable (x), use X,T,θ,n. • To generate the graph of a function, use GRAPH after entering the function. The screen capture above is how the graph of 1 11y x=+ − will look like in the ZStandard ( ZOOM 6 ) setting. Notice that the asymptotes are not displayed. 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 In fact, the GC is not able to display asymptotes. Any asymptotes will have to be drawn based on your understanding of the graph and the function it represents. In other words, you SHOULD NOT BE RELIANT on the GC to s how every feature of the graph of a function. That being said, the GC can still be used to provide an idea of what the asymptotes might be. This needs to done in conjunction with: • Your knowledge of the graph and the function it represents. • The visual observations made on the graph displayed using appropriate WINDOW and ZOOM settings (we shall look at this at a later stage of the lesson). • An understanding of the definition of different types of asymptotes. Analysing horizontal asymptotic behaviour Recall that a horizontal asymptote is a line with equation yk= , where k is the value a function approaches as x approaches + and − , and may or may not be the same at + and − . With this understanding, we can use the GC to observe what happens to the value of a function when x is an extremely large positive value and an extremely negative value. This will allow us to identify possible asymptotic behaviour(s). To determine what happens to 1 11y x=+ − when x becomes an extremely large positive value: • Press 2ND Window to access the TABLE SETUP of the GC. • Enter an extremely large positive TBLSTART value of x for e.g. 1 2ND , 9 9, which is 1E99 i.e 9910 . • Press 2ND GRAPH and observe the values. Change this value

2025 Year 4 Math / Graphs Unit 16 Graphing with GC Page 3 • Observations ✓ The values of x simulates the event where x approaches + . ✓ The values of y are observed to “constantly” be 1y= , which is the value y appro