1. **State the problem:** We are given the function $f(x) = \frac{3x - 5}{x - 2}$ and asked to analyze or simplify it. 2. **Formula and rules:** This is a rational function, which is a ratio of two polynomials. Important rules include domain restrictions where the denominator cannot be zero. 3. **Find the domain:** The denominator $x - 2 \neq 0$ so $x \neq 2$. 4. **Simplify the function if possible:** $$f(x) = \frac{3x - 5}{x - 2}$$ No common factors to cancel, so the function is already simplified. 5. **Interpretation:** The function is defined for all real $x$ except $x=2$ where there is a vertical asymptote. 6. **Optional: Find intercepts** - **x-intercept:** Set numerator to zero: $$3x - 5 = 0 \implies x = \frac{5}{3}$$ - **y-intercept:** Set $x=0$: $$f(0) = \frac{3(0) - 5}{0 - 2} = \frac{-5}{-2} = \frac{5}{2}$$ Final answer: The function is $f(x) = \frac{3x - 5}{x - 2}$ with domain $x \neq 2$, x-intercept at $\left(\frac{5}{3}, 0\right)$, and y-intercept at $(0, \frac{5}{2})$.