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Please write a rational expression (in factored form please) that could produce this graph. Please note that the graph reaches the x axis at -1. Explain your reasoning for each factor your write.

Please write a rational expression (in factored form please) that could produce this graph. Please note that the graph reaches the x axis at -1. Explain your reasoning for each factor your write.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please write a rational expression (in factored form please) that could produce this graph.  Please note that the graph reaches the x axis at -1.  Explain your reasoning for each factor your write.

Please write a rational expression (in factored form please) that could produce this graph. Please note that the graph reaches the x axis at -1. Explain your reasoning for each factor your write. -10 45 40 35 30 25 20 15 10 5 =5 -10 -15 -20 -25 -30 -35 40 -50 10 12 x
Transcribed Image Text:Please write a rational expression (in factored form please) that could produce this graph. Please note that the graph reaches the x axis at -1. Explain your reasoning for each factor your write. -10 45 40 35 30 25 20 15 10 5 =5 -10 -15 -20 -25 -30 -35 40 -50 10 12 x
Expert Solution
Step 1

From the above graph, we see that the graph goes to ∞ when x→2+ and the graph goes to -∞ when x→2-.

So, the function must have the term 1x-2.

Further, we are given that the graph reaches the x axis at -1.

So, the function must have the term (x+1).

Now, notice that the graph decreases linearly for x<-2 and the graph is increasing linearly for x>5.

So, we must have the term (x-a) where the value of a is to be found.      

Thus, the possible equation of function is f(x)=(x+1)(x-2)(x-a).

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