Answered: What is the equation for the horizontal…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.6: Rational Functions

Problem 91E

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Question

What is the equation for the horizontal asymptote of the rational functional graph?

1) y=2

2)Y=3

3)Y=0

4)X=3

5)X=2

6)X=0

Expert Solution

Step 1

The domain of the given function is,

$D = \{x | x \neq 2\}$

The rage of the function is,

Step 2

The horizontal asymptote is a horizontal line in a graph of function 'f(x)'. The function approaches a horizontal line with the expression 'y=c' when x tends to infinity or negative infinity.

From the above definition and the graph,
The function tents to a constant 'y=3' when x tends to infinity or negative infinity.

Thus, the expression of horizontal asymptote is y=3. The correct option is option (3) Y=3.

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