1. **State the problem:** We are given the function $$f = 5x^2 + \sqrt{9x - x - 3} - x - 3$$ and asked to understand and graph it. 2. **Simplify inside the square root:** Simplify the expression inside the square root: $$9x - x - 3 = 8x - 3$$ 3. **Rewrite the function:** Now the function is: $$f = 5x^2 + \sqrt{8x - 3} - x - 3$$ 4. **Domain considerations:** The square root requires the radicand to be non-negative: $$8x - 3 \geq 0 \implies x \geq \frac{3}{8}$$ 5. **Summary:** The function is defined for $$x \geq \frac{3}{8}$$ and is: $$f(x) = 5x^2 + \sqrt{8x - 3} - x - 3$$ 6. **Graphing notes:** The function combines a quadratic term, a square root term, and linear terms. The quadratic term dominates for large $$x$$, so the function grows quickly. Final answer: $$f(x) = 5x^2 + \sqrt{8x - 3} - x - 3, \quad x \geq \frac{3}{8}$$