Consider the following ''monster'' rational function. f(x)=\frac{x^{2}-3x^{3}-21x^{2}+43x+60}{x^{4}-6x^{3}+x^{2}+24x-20} Analyzing this function will synthesize

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Consider the following monster rational function.
Analyzing this function will synthesize many of the concepts of this and earlier sections.

Answer & Explanation



Expert2022-01-19Added 681 answers

Step 1 We can first factor the numerator and express f(x) as: f(x)=x216x+4 =(x+4)(x4)(x+4) =x4 With this, the graph of the rational function would be similar to the graph of f(x)=x4 Step 2 Since there is a factor x+4 on both the numerator and denominator, we can say that there is a hole on the graph of f(x) Step 3 To find the x-coordinate of the hole, we just solve for x in x+4=0 x+4=0 x=4 Step 4 To find the y-coordinate of the hole, we solve for f(x)=x4 with x=4 f(4)=x4=44=8 Step 5 Thus, we can say that the graph has a hole at the coordinates: (4, 8)

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