Reciprocal Functions

f(10) =

f(10) = 1/f(10) = 1/10 = 0.1

f(5) = 5

f(5) = 5 1/f(5) = 1/5 = 0.2

f(4) = 4

f(4) = 4 1/f(4) = 1/4 = 0.25

f(2) = 2

f(2) = 2 1/f(2) = 1/2 = 0. 5

f(1) = 1

f(1) = 1 1/f(1) = 1/1 = 1.0

f(0.6) = 0.6

1/f(0.6) = 1/0.6 = 1.33 f(0.6) = 0.6

f(0.2) = 0.2

1/f(0.2) = 1/0.2 = 5.0 f(0.2) = 0.2

1/f(x) = 1/x The function ‘f(x)’ is transformed. Big values of f(x) become small fractions; small fractions become big numbers 1/f(x) = 1/x

1/f(x) will never reach a value of zero, but it will ‘approach’ a value of zero at infinity. The line that a curve approaches at infinity is called an ‘asymptote’ 1/f(x) = 1/x

The value of 1/f(x) when x is zero is undefined: doesn’t exist. There is an ‘asymptote’ on the y-axis too that the curve never quite reaches. 1/f(x) = 1/x