Page 62 - Math SL HB Sem 1

FUNCTIONS, EQUATIONS, INEQUALITIES

5. THE RECIPROCALFUNCTION
l,*
Oneinteresting lunction is /(x)= 0
.)( "

This graph has a shape known as a rectangular hyperbola. The horizontal and vertical
asymptotes ofthe basic function .f(r) ,L ,x I 0 can also be 'relocated'.
x

'[ he inverse function ot 1 i. /'(*)=],*
/(x) =
xx * O,
i... (f '(r)) =, 1 =.r <+ (i
"f = .[" =l . Then, as the two f-r (x) functions are identical, it is
x
its sell-inverse.

Sketchingthe graph of 11i =!,* s g and reflecting it about the linc y =;5 y7;11 show lhat the
x
two graphs overlap each other. v

I
x

x

Example I
Sketch the graph of the following function

a)f(x)- | ,-z
x-l

b)f(x)-2-?
x

j- ri