Exponential Functions and

Graphs

13

15.1 Introduction

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Building on the previous two chapters, we willdiscuss the sketching and interpretation of the graphs

of general exponential functions in this chapter.

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

13.2 Functions of the Form

y=ab

(x+p)

+q for b> 0

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This form of the exponential function is slightlymore complex than theform studied in Grade 10.

1

2

3

4

4 3 − 2 − − 1 − 1 2 3 4

Figure 13.1: General shape and position of thegraph of a function of the form f(x) = ab(x+p)+ q.

Activity: Functions of the Formy=ab(x+p)+q

1. On the same set of axes, plot the following graphs:
   (a) a(x) =− 2 (x+1)+ 1
   (b) b(x) =− 1 (x+1)+ 1
   (c) d(x) = 1(x+1)+ 1
   (d) e(x) = 2(x+1)+ 1
   Use your results to deduce the effect of a.


2. On the same set of axes, plot the following graphs:
   (a) f(x) = 2(x+1)− 2