In this section, you will learn how to graph rational functions with holes.
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Now let us take an example and understand "How to graph rational functions with holes".
Graph the rational function given below.
Step 1 :
First, we have to find hole, if any.
To find hole of the rational function, we have to see whether there is any common factor found at both numerator and denominator.
So, let us factor both numerator and denominator.
y = [(x - 2)(x + 1)] / (x - 2)
In our problem, clearly there is a common factor
(x - 2)
found in both numerator and denominator.
So, there is a hole.
Step 2 :
Now, we have to cross out the common factor (x - 2) at both numerator and denominator as given below.
Step 3 :
Now we have to make the common factor (x - 2) equal to zero.
When we do so, we get
x - 2 = 0
x = 2
So, the hole is at x = 2.
Step 4 :
After having crossed out the common factor (x - 2), the function is simplified to
f(x) = x + 1
y = x + 1
Step 5 :
Substitute 2 for x in y = x + 1.
y = 2 + 1
y = 3
So, the hole appears on the graph at (2, 3).
Step 6 :
In y = x + 1, now we have to plug some random values for "x" and find the corresponding values of "y" as given in the table below.
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