1. **Problem Statement:** We have a company's cost function $C = 2x + 100$ and revenue function $R = 5x$. We need to graph both functions and find the break-even point. 2. **Formulas and Explanation:** - Cost function: $C = 2x + 100$ means the company has a fixed cost of 100 and a variable cost of 2 per unit. - Revenue function: $R = 5x$ means the company earns 5 per unit sold. - The break-even point occurs where revenue equals cost: $R = C$. 3. **Finding the Break-even Point:** Set $5x = 2x + 100$. 4. **Solving for $x$:** $$5x = 2x + 100$$ $$5x - 2x = 100$$ $$3x = 100$$ $$x = \frac{100}{3} \approx 33.33$$ 5. **Interpretation:** At approximately 33.33 units sold, the company's revenue equals its cost, meaning it neither makes a profit nor a loss. Selling more than this number of units results in profit. 6. **Summary:** - Cost function: $C = 2x + 100$ - Revenue function: $R = 5x$ - Break-even point: $x = \frac{100}{3} \approx 33.33$ This is the point where the company covers all costs exactly.