A Rational Function is a function which is in the form of p / q. Here 'p' and 'q' are two Polynomials. It is very difficult to graph a rational function. For this we have to find 'x' and 'y' intercepts of rational function. First we define these points where they are undefined then we calculate intercepts of rational function. Let us see the procedure of finding x intercepts of rational Functions.
Step 1: Take a rational function whose intercepts we have to calculate.
Step 2: Move all terms of 'y' on one side of equation and terms of 'x' on other side of equation.
Step 3: For calculating x- intercepts put value of 'y' as zero.
Step 4: For calculating y- intercepts put value of 'x' as zero.
Step 5: Apply cross multiplication to find value of intercept.
Step 6: Put value of one intercept in equation to find value of other intercepts.
It will be easy to understand the procedure of finding x- intercept with help of an example. So let us take an example. We are given a rational function y = (4x + 6) / (x - 2).
Now we will put value of 'y' equals to zero in order to get x- intercepts:
0 = (4x + 6) / (x - 2).
Now by cross multiplication (x - 2) becomes zero and equation becomes: 0 = 4x + 6.
Now we can calculate value of x- intercept as:
0 = 4x + 6,
-6 = 4x,
-6 /4 = x,
x = -3 / 2.
This graph will intersect x- axis at Point -3 /2.