Rational Function 721954

1. **State the problem:** We need to determine if the expression $$y=\frac{3x+4}{x-2}$$ defines a function. 2. **Recall the definition of a function:** A function assigns exactly one output value for each input value in its domain. 3. **Analyze the given expression:** The expression is a rational function where the numerator is $$3x+4$$ and the denominator is $$x-2$$. 4. **Domain considerations:** The denominator cannot be zero because division by zero is undefined. So, $$x-2 \neq 0 \Rightarrow x \neq 2$$. 5. **Conclusion:** For every $$x$$ except $$x=2$$, there is exactly one output $$y$$. Therefore, $$y=\frac{3x+4}{x-2}$$ is a function with domain $$\{x \in \mathbb{R} : x \neq 2\}$$. **Final answer:** Yes, $$y=\frac{3x+4}{x-2}$$ is a function.