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What is the equation of the vertical asymptote of y=1x+9y = \frac{1}{x + 9} ? _____

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Q. What is the equation of the vertical asymptote of y=1x+9y = \frac{1}{x + 9} ? _____
  1. Identify vertical asymptote condition: Identify the condition for a vertical asymptote in a rational function. A vertical asymptote occurs where the denominator of the function is equal to zero, since the function is undefined at that point. For the given function y=1x+9y = \frac{1}{x + 9}, the denominator is x+9x + 9.
  2. Set denominator equal to zero: Set the denominator equal to zero to find the value of xx where the vertical asymptote occurs. The equation to solve is x+9=0x + 9 = 0.
  3. Solve for x: Solve the equation x+9=0x + 9 = 0 for xx by subtracting 99 from both sides. This gives x=−9x = -9.
  4. Location of vertical asymptote: The value of xx found in the previous step is the location of the vertical asymptote. Therefore, the equation of the vertical asymptote is x=−9x = -9.

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