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Exploring Cubic and Rational Functions: A Graphing Guide

Learn to identify, graph, and solve cubic and rational functions accurately using a Graphical Display Calculator. Practice with examples and homework exercises provided in this comprehensive math resource.

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Exploring Cubic and Rational Functions: A Graphing Guide

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  1. Material Taken From:Mathematicsfor the international student Mathematical Studies SLMal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark BruceHaese and Haese Publications, 2004

  2. Objectives To identify a cubic and a rational function and their properties. To accurately graph unfamiliar functions. To find the solutions using the GDC.

  3. Opening Problem

  4. Families of Functions

  5. Families of Functions

  6. Things to pay attention to when graphing functions: x- and y- intercepts maxima and minima asymptotes, if they exist

  7. Section 17A - Cubic Function • www.explorelearning.com • For demo purposes only: • Cubic Functions • Polynomials

  8. Example 1 Consider the function: y = 2x3 – 17x2 + 42x – 30 Find the axes intercepts Find the coordinates of any turning points Sketch the graph of the function, highlighting the key features found above.

  9. Section 17C - Rational Function • www.explorelearning.com • For demo purposes only: • Rational Function

  10. Example 2 Consider the function: Find the asymptotes of the function Find the axes intercepts Sketch the function, include the key features found above.

  11. Homework • 17A.1 – Pg 549 • #1ach, #2ac • 17A.3 – Pg 552 • #1bd • 17A.4 – Pg 552-553 • #1,5 • 17C.1 – Pg 559 • #1, 3abc • 17C.2 – Pg 561 • #1bd, 3ad • 17C.3 – Pg 562 • #1,2

  12. Section 17E – Unfamiliar Functions Section 17F – Where Functions Meet Find where the line y = x – 3 meets Example 3

  13. Accurate Graphing • On the IB exam you will be expected to: • draw accurate graphs of • linear • quadratic • exponential and • trigonometric functions • use the GDC to sketch and analyze some simple unfamiliar functions • e.g. cubic and rational

  14. Homework • 17E – Pg 565 • #1 • 17F.1 – Pg 567-568 • #1ac, 2ac, 4ae, 6abc • 17F.2 – Pg 569 • #1cf, 2ab • IB Examples Worksheet

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