Decide whether each relation defines \( y \) as a function of \( x \). Give the dornain and range. \( y=\frac{3}{x-3} \) Does this relation give a function? Yes No What is the domain? (Type your answer in interval notation.) What is the range? (Type your answer in interval notation.)

Yes, this relation does define \( y \) as a function of \( x \) since for each input \( x \) (except for where the function is undefined), there is exactly one output \( y \). The domain of the function \( y = \frac{3}{x-3} \) excludes the value that makes the denominator zero. Thus, \( x - 3 \neq 0 \) leads to \( x \neq 3\). In interval notation, the domain is \( (-\infty, 3) \cup (3, \infty) \). For the range, as \( x \) approaches 3 from the left, \( y \) approaches negative infinity, and as \( x \) approaches 3 from the right, \( y \) approaches positive infinity. The function cannot equal zero, as there is no value of \( x \) that makes \( y \) equal to zero. So, the range is \( (-\infty, 0) \cup (0, \infty) \).