anonymous
  • anonymous
Which of the following is true for the rational function shown in the graph below?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@jazzyfa30
mathstudent55
  • mathstudent55
Look at the answers with asymptotes. Does either one make sense?
anonymous
  • anonymous
nop i know it has to be either B or D

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mathstudent55
  • mathstudent55
Ok. Look at B. Can you factor the denominator?
anonymous
  • anonymous
yes
mathstudent55
  • mathstudent55
Show me.
anonymous
  • anonymous
mathstudent55
  • mathstudent55
That's the numerator.
anonymous
  • anonymous
xD Whoops
mathstudent55
  • mathstudent55
Look at the denominator of B. x^2 + 16 Can this denominator be zero? Is there any value of x that would make this denominator zero?
anonymous
  • anonymous
mathstudent55
  • mathstudent55
Now quite: (x + 4)(x + 4) = (x + 4)^2 = x^2 + 8x + 16 You have x^2 + 16, without the middle term of 8x.
mathstudent55
  • mathstudent55
(x - 4)(x - 4) doesn't work either: (x - 4)(x - 4) = x^2 - 8x + 16 Again, there is amiddle term here that your problem does not have.
anonymous
  • anonymous
2
anonymous
  • anonymous
(x-2)(x-2)
mathstudent55
  • mathstudent55
x^2 + 16 for x = 2: 2^2 + 16 = 4 + 16 = 20
mathstudent55
  • mathstudent55
Ok. Let's look at B. The denominator cannot be factored. x^2 + 16 cannot be factored. Now think this way: The only way x^2 + 16 could equal zero is if x^2 = -16, since -16 + 16 = 0. But x^2 cannot equal a negative number. That means, there is no value of x that can make x^2 + 16 equal zero. Since x^2 + 16 is in the denominator, and the denominator cannot be zero, B has no asymptotes.
mathstudent55
  • mathstudent55
Now look at D: The denominator is x^2 - 16. x^2 - 16 factors into (x + 4)(x - 4) That means when x = -4 or x = 4, x^2 - 16 equals zero. That means x = -4 and x = 4 are not allowed. That means there is an asymptote at x = -4 and an asymptote at x = 4.
anonymous
  • anonymous
ok so d is the answer
mathstudent55
  • mathstudent55
Right.

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