Consider the following monster rational function. f(x)=x2−3x3−21x2+43x+60x4−6x3+x2+24x−20 Analyzing this function will synthesize many of the concepts of this and earlier sections.

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Consider the following monster rational function.  f(x)=x2−3x3−21x2+43x+60x4−6x3+x2+24x−20  Analyzing this function will synthesize many of the concepts of this and earlier sections.

nick1337 · Accepted Answer

Step 1 We can first factor the numerator and express f(x) as: f(x)=x2−16x+4 =(x+4)(x−4)(x+4) =x−4 With this, the graph of the rational function would be similar to the graph of f(x)=x−4 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)=x−4 with x=−4 f(−4)=x−4=−4−4=−8 Step 5 Thus, we can say that the graph has a hole at the coordinates: (−4, −8)

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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