Finding the rational function by using the graph Assignment: Find a possible function f(x) which gives the following graph:ESATANZANIA JUMATI1001 MOLION M+8antur us F પાવા104ATIMINTHA SHEHBUMINITEZHEITIRMEONE TOIM 2010:1000|||09|4|02||29|161100JPlease note that this graph has vertical asymptotes of a = -1 and 2 = 3.

If the graph of the function f(x) intersects x axis at x=a, then (x-a)m is a factor of f(x) and will…

Answered: Assignment: Find a possible function…

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Finding the rational function by using the graph

Expert Solution

Step 1

If the graph of the function f(x) intersects x axis at x=a, then (x-a)^m is a factor of f(x) and will be present in the numerator part of the function expression of f(x).
If there is a vertical asymptote at the x=b then (x-b)ⁿ is in the denominator of the function f(x), further if the graph around the asymptotes lie in the same quadrant or direction of the asymptote then n is even, if the graph lie in the opposite direction of the asymptote then n is odd.
Let Degree of numerator of the f(x) be N and Degree denominator of the f(x) be D.
1. if N<D, then horizontal asymptote is y=0
2. if N=D,then horizontal asymptote is y= ratio of leading coefficients.
3. if N>D, then horizontal asymptote do not exist.