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

Mathematics

2 answers:

MAVERICK [17]2 years ago

8 0

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}

xxMikexx [17]2 years ago

3 0

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.

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2 years ago

40.51x+12.45y=666.64

irga5000 [103]

Answer:

The graph of the equation 40.51x+12.45y=666.64 is attached with the answer where the horizontal axis represents the X axis and the vertical axis represents Y axis.

To plot the graph physically just find two points lying on the line. Mark the points on the graph sheet and then join them. This will give you the line represented by the equation.

To find points on the line assume the value of any one variable, substitute it in the equation, then solve the equation to find the value of other variable. For example : assume y = 1; substitute the value of y in the equation;

⇒ 40.51x + 12.45×1 = 666.64

⇒ 40.51x = 666.64 - 12.45

⇒ 40.51x = 654.19

⇒ x = $\frac{654.19}{40.51}$

⇒ x ≈ 16.149

Therefore point ( 16.149 , 1 ) lie on the graph of the equation.

***Only two points are required to plot this graph just because it represents a straight line, that we can conclude just by observing the equation. If in an equation the power of x is 1 or 0 and power of y is 1 or 0 then only it will represent a straight line in 2-D plane.***