Suppose we have a rational function f (u) = u2 - 4 / u2 – 4u, then we can plot graph of rational function as shown below.
Solution: - To plot graph of this function we need to follow some steps.
Step 1: First of all check whether the function is rational function or not. According to the definition of rational functions it is ratio of two polynomials. So rational function is:
=> f (u) = u2 - 4 / u2 – 4u,
Here in this above function we cannot put value of denominator as zero because when we put value of denominator as zero then whole function changes to infinity. y – intercept will not be present in graph.
Step 2: Put numerator value equals to zero to obtain the value of 'x'.
So we can write numerator value as:a
=> u2 – 4 = 0, so here we get two values of 'u' that is u = + 2.
Above function can also be written as:
= u2 – 4 = u (u – 4) = 0, so here we get value of 'u' as 0 and 4.
Step 3: Now put different values of 'u' to get more values.
When we put values of 'u' as 1, 3 and 5 then we get other values 1, -5 / 3 and 21 / 5 respectively. Using these coordinates value we can plot graph of rational function. Graph of rational function is shown below:
This is how we plot simple rational function graph.