Decide whether each relation defines \( y \) as a function of \( x \). Give the domain and range. \( y=\frac{3}{x-3} \)

We are given the equation y = 3/(x - 3). Step 1. Is it a function? Yes, it is a function because for each valid input x (where the expression is defined) there exists exactly one corresponding output y. Step 2. Determine the domain. The denominator cannot be zero. Set x - 3 ≠ 0, which implies that x ≠ 3. • Domain: { x ∈ ℝ : x ≠ 3 }. Step 3. Determine the range. To find the range (all possible y values), note that if y = 3/(x - 3), then y can take any real value except one specific value that can’t be reached. Solve for x to see a constraint:   y = 3/(x - 3)   => x - 3 = 3/y (provided y ≠ 0)   => x = 3 + 3/y. When y = 0, the equation 3 = 0 (from 3/(x-3)=0) would be impossible. Thus, y cannot equal 0. • Range: { y ∈ ℝ : y ≠ 0 }. Final Answer: The relation defines y as a function of x. • Domain: All real numbers except 3. • Range: All real numbers except 0.