anonymous
  • anonymous
Which of the following is false for f(x) = (10x^3 - 10x^2 - 10x) / (2x^5 - 2x) ? (a) The y-axis is not an asymptote of f(x). (b) The x-axis is an asymptote of f(x). (c) x = –1 is not an asymptote of f(x). (d) x = 1 is an asymptote of f(x). So, I took a quiz that had this question and I, of course, got it wrong. The first time that I took the quiz, it had a similar question to the one above and the second time I had taken it, it had this exact one. For the question above, I chose answer choice (a), because the first time I had chosen (c). Can someone PLEASE help me?
Mathematics
katieb
  • katieb
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campbell_st
  • campbell_st
well if you factor the numerator and denominator you get \[f(x) = \frac{10x(x^2 - x -1)}{2x(x^4 - 1)} = \frac{5(x^2 - x - 1)}{x^4 - 1}\] so the function has vertical asymptotes at x^4 = 1 or x = -1 and x = 1
campbell_st
  • campbell_st
there is a point of discontinuity at x = 0 since the degree of the denominator is greater than the degree of the numerator y = 0 is an asymptote so the x-axis is an asymptote
campbell_st
  • campbell_st
so the point of discontinity is the y- intercept (0, 5) so I think the curve is |dw:1442175602395:dw|

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campbell_st
  • campbell_st
the point of diswingspaninuity occurs because you factor 10x in the numerator and 2x in the denominator... which simplifies to 2
anonymous
  • anonymous
Would the answer then be (c) because x = -1 is an asymptote of f(x)? Because if it is, I don't know why it told me that I got the answer wrong the first time.
campbell_st
  • campbell_st
well the question asks, which is false...
campbell_st
  • campbell_st
so I think its A
campbell_st
  • campbell_st
well its A or B I just checked the graph |dw:1442176003475:dw|
campbell_st
  • campbell_st
you cam graph the curve using https://www.desmos.com/calculator and make your own decisions.
anonymous
  • anonymous
Well, I chose (a) and it said that that was the wrong answer, too. So I'm kind of confused.
anonymous
  • anonymous
Either way, thanks for the help :) @campbell_st

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