Show all work to identify the asymptotes and zero of the function f(x)=6x/x^2-36

9514 1404 393

  asymptotes: x = ±6

  zero: x = 0

Step-by-step explanation:

The vertical asymptotes of the function will be at the values of x where the denominator is zero. The denominator is x^2 -36, so has zeros for values of x that satisfy ...

  x^2 -36 = 0

  x^2 = 36

  x = ±√36 = ±6

The vertical asymptotes of the function are x = -6 and x = +6.

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The zero of the function is at the value of x that makes the numerator zero. This will be the value of x that satisfies ...

  6x = 0

  x = 0 . . . . . divide by 6

The zero of the function is x=0.

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As a check on this work, we have had a graphing calculator graph the function and identify the zero.

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