Word Count : 438

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To find the largest possible domain and corresponding range of the function: \[ f(x) = \frac{x-2}{3-x} \] ### Step 1: Find the domain of the function The domain of the function consists of all real values of \( x \) for which the denominator is not zero, since division by zero is undefined. The denominator is \( 3 - x \). Set the denominator equal to zero to find when the function is undefined: \[ 3 - x = 0 \] \[ x = 3 \] Therefore, the function is undefined when \( x = 3 \). Hence, the domain of the function is all real numbers except \( _____ ________ _____ __________ _______ __________ _____ ___.
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