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Chapter 4: Q. 5 (page 234)

True or False.

The graph of a rational function sometimes

has a hole.

Short Answer

Expert verified

The given statement istrue.

Step by step solution

01

Step 1 Sometimes rational function which is of the form pqwhere q≠0 and q has some factors which are divisible by the numerators.

Consider an example,fx=x2-2x-3x2-9.

Let us factor it.

fx=x+1x-3x+3x-3.

02

Step 2 Now look at the example.

In the example,x-3is the factor and x=3is the hole of this rational polynomial.

This means that on the graph of this function, this point will not exist and we will have to represent that with a hole on the graph.

Therefore, sometimes rational function have a hole.

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