Module 1: Reciprocal function graphs

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Advanced Mathematics - Graphs of reciprocal functions

Graphs of reciprocal functions

The features of reciprocal graphs are summarised in the following table:

FEATURES OF ORIGINAL GRAPHS, F(X)
FEATURES OF RECIPROCAL GRAPHS 1/F(X)

y intercept at y = a
y intercept at y = 1/a

x intercepts at x = b and x = c
Vertical asymptotes at x = b and x = c

Vertical asymptote at x = d
Point discontinuity on the X axis at x = d

Maximum turning point at (f,g)
Minimum turning point at (f,1/g)

Any value of x where y = 1
Same point on reciprocal graph

As original graph f(x) approaches infinity
Reciprocal graph approaches zero so x axis (y = 0) is an asymptote

As original graph f(x) approaches zero
Reciprocal graph approaches infinity

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