Rational functions are basically a division of a polynomial function with another polynomial function.
f(x)= s(x)/ r(x)
Where f(x), s(x) and r(x) are polynomial functions, r(x) cannot be zero and the degree of r(x) > 0.
The simplest rational function is of the form f(x) = y = k/x where k is a constant. It is also called the inverse
variation function because y varies inversely with x which means that as the value of x increases, that of y
xy = k can be written as y = k/x and hence represents an inverse relation between x and y.
The rate of flow of water through a pipe is x cm3 per second. Express the time required to fill a tank of volume k
cm3 as a function of x.
We can solve this problem by using the unitary method.
The time required to fill x cm3 of water in the tank = 1 second.
Time required to fill 1 cm3 of water in the tank = 1/x second.
t = time required to fill k cm3 of water in the tank = k/x second.
t = k/x; therefore, time varies inversely with x.
You will encounter rational expressions in many problems related to the ratio of two quantities.
Try this problem
Find the ratio of the area of rectangle A with dimensions 4x and 4x+8 to Rectangle B with dimensions 2x and 2x +2.
Area of rectangle A ÷ Area of rectangle B =