Question

What is the first step in sketching the graph of a rational function?

Answer 1

Consider the rational function

     $f(x)=\frac{P(x)}{Q(x)}$

We will find the Domain of Rational function first, means those value of  rational function for which f(x) is defined, To do this we will evaluate those  point first for which, Q(x)=0.

So, The first Step is "Finding Domain of the rational function" as well as the point where function is not defined.

⇒Consider the function

    $f(x)=\frac{x-3}{x-2}$

→Domain of the function is

x-2=0

x=2

=All Real Numbers , except at x=2.

=R- {2}

Answer 2

Answer:

Step-by-step explanation:

Find the x-value that makes the denominator zero.  This x = a is the equation of the vertical asymptote.  Next, determine the behavior of the function as x increases without bound in either direction.  If there is a limiting value, then this y = d is the horizontal asymptote.