Hyperbolic Functions and

Graphs

12

13.1 Introduction

EMBBD

In the previous chapter,we discussed the graphsof general quadratic functions. In this chapter we will

learn more about sketching and interpreting thegraphs of general hyperbolic functions.

See introductory video:VMfmc at http://www.everythingmaths.co.za

12.2 Functions of the Form y =xa+p+ q

y=

a

x+p

+q

EMBBE

This form of the hyperbolic function is slightly more complex than the form studied in Grade 10.

1

2

3

4

5

− 1

− 2

− 3

− 4

− 5

5 4 − 3 − 2 − − 1 − 1 2 3 4 5

Figure 12.1: General shape and position of thegraph of a function of the form f(x) =x+ap+ q. The

asymptotes are shown as dashed lines.

Activity: Functions of the Formy=

a

x+p+q