### Lesson 4: Reciprocal

(A)  Introduction

Basically this transformation involves taking the reciprocal of the original y coordinates of the graph. It will be useful to memorise how the key features of the original graph are transformed before we insert the new graph.

Note:

In this section the notation a   represents a value slightly larger than a.

a   represents a value slightly smaller than a.

+

_

(B)  Transformation of features

y = f (x)

(I)

Vertical asymptote x = k

(II)

Horizontal asymptote y = b,

b is non zero

(III)

Oblique asymptote y = mx + c

(IV)

Max point (a, b)

(V)

f (x) is increasing

(VI)

f (x) = a

+

x intercept (k, 0)

Horizontal asymptote y = 1/b

Horizontal asymptote y = 0

Min point (a, 1/b)

1 /f (x) is decreasing

1/f (x) = (1/a)

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Example 1

Given the following graph of y = f (x), sketch the graph of y = 1/f (x).

Solution

Example 2

Given the following graph of y = f (x), sketch the graph of y = 1/f (x).

Solution

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