Decide whether each relation defines \( y \) as a function of \( x \). Give the domain and range. \( y=\frac{3}{x-3} \) Does this relation give a function? \( \begin{array}{l}\text { Yes } \\ \text { No } \\ \text { What is the domain? } \\ \text { (Type your answer in interval notation.) } \\ \text { What is the range? } \\ \text { (Type your answer in interval notation.) }\end{array} \) (1)

Yes, this relation does define \( y \) as a function of \( x \) because for every input \( x \) (except \( x=3 \), where the function is undefined), there is exactly one output \( y \). The domain of the function is all real numbers except \( x=3 \), which can be expressed in interval notation as \( (-\infty, 3) \cup (3, \infty) \). The range is all real numbers except \( y=0 \), since \( y \) approaches zero but never actually reaches it as \( x \) approaches positive or negative infinity, resulting in the range \( (-\infty, 0) \cup (0, \infty) \).