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What is the excluded value for $y = \frac{1}{x - 9} - 9 ?$ $\newline$ _____

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Rational functions: asymptotes and excluded values

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Q. What is the excluded value for

y = \frac{1}{x - 9} - 9 ?

\newline

_____

Identify denominator: Identify the denominator of the fraction in the function to determine the value for which the function is undefined. $\newline$ y = $\frac{1}{x - 9}$ - $9$ $\newline$ The denominator of the fraction is $x - 9$ .
Set denominator to zero: Set the denominator equal to zero to find the value of $x$ that cannot be used in the function. $x - 9 = 0$ Solve for $x$ to find the excluded value.
Solve for excluded value: Add $9$ to both sides of the equation to isolate $x$ . $\newline$ $x - 9 + 9 = 0 + 9$ $\newline$ $x = 9$ $\newline$ The excluded value is $9$ , as this would make the denominator zero, which is undefined in real numbers.

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