Rational Function B60523

1. **State the problem:** Determine if the expression $$y=\frac{3x+4}{x-2}$$ represents 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:** $$y=\frac{3x+4}{x-2}$$ is a rational expression where the denominator cannot be zero. 4. **Find the domain:** The denominator $$x-2$$ cannot be zero, so $$x \neq 2$$. 5. **Check if for each valid input $$x$$ there is exactly one output $$y$$:** For every $$x \neq 2$$, the expression yields exactly one value of $$y$$. 6. **Conclusion:** Since for every $$x$$ in the domain (all real numbers except $$2$$) there is exactly one output $$y$$, the expression defines a function. **Final answer:** Yes, $$y=\frac{3x+4}{x-2}$$ is a function with domain $$\{x \in \mathbb{R} : x \neq 2\}$$.