Topic Two (1.2): Rational Functions and Graphs

Introduction Icon.png Introduction

A rational function is any function which is the quotient (result of dividing) of two polynomials. Here is a good link summarising what they are and how we explore them:

EXPLORE - Rational Expressions (MathsIsFun) Links to an external site.

In this topic we shall look at how to sketch graphs of rational functions, particularly looking at how to find asymptotes and holes, including oblique (slant) asymptotes.

Read Icon.png Reading

For this topic, you will need to work through pages 16 to 44 of your textbook.

Activities Icon.png Pre-requisite Knowledge

Check the prerequisite knowledge section on page 17 and refer back to the A Level material if needed.

Additional resources on these topics can be found via the following links:

READ – Polynomial Division (Math Tutor) Links to an external site.

EXPLORE – Transformations of Graphs (Underground Mathematics) Links to an external site.

WATCH - Partial Fractions: Introduction and Basic Concepts (YouTube) Links to an external site.

WATCH - Partial Fractions: A Range of Worked Examples (YouTube) Links to an external site.

WATCH - Asymptotes: Horizontal and Vertical (YouTube) Links to an external site.

WATCH - The Modulus Function Playlist (YouTube) Links to an external site.

Read & Make Notes Icon.png Tasks

Complete the following:

  • Investigate the topic using the interactive activity on Desmos:

EXPLORE – Rational Functions in the form f(x)=(ax+b)/(cx+d) (Desmos) Links to an external site.

  • Read pages 17 to 23 and try exercise 2A.
  • Read pages 24 to 28 and try exercise 2B on oblique asymptotes.
  • Read pages 29 to 33 and try exercise 2C on inequalities.
  • Read pages 34 to 41 and try exercise 2D.
  • Check your understanding using the interactive worksheet on Desmos:

COMPLETE –Rational Functions (Desmos) Links to an external site.

Consolidate Icon.png Consolidate

Now consolidate your understanding by making revision cards for this chapter (the checklist on page 43 will help) and work through the end-of-chapter review on page 44.

For further support, try the following links:

WATCH & EXPLORE – Rational Functions (Khan Academy) Links to an external site.

WATCH – Graphing Rational Functions (YouTube) Links to an external site.

EXPLORE – Asymptotes of Rational Functions (GeoGebra) Links to an external site. [Not currently available]

READ – Graphing Rational Functions (Varsity Tutors) Links to an external site.

READ – Graphing Rational Functions (Coolmath) Links to an external site.

READ – Solving Rational Inequalities (Paul’s Online Notes) Links to an external site.