**Problem 7:** Evaluate function values at given points. Since the exact function is not given for problem 7, I assume it corresponds to problem 15: $f(x) = 2x^2 - 7x - 30$ (based on numbering). 1. Calculate $f(-2)$: $$f(-2) = 2(-2)^2 - 7(-2) - 30 = 2(4) + 14 - 30 = 8 + 14 - 30 = -8$$ 2. Calculate $f(-1)$: $$f(-1) = 2(-1)^2 - 7(-1) - 30 = 2(1) + 7 - 30 = 2 + 7 - 30 = -21$$ 3. Calculate $f(\frac{1}{2})$: $$f(\frac{1}{2}) = 2(\frac{1}{2})^2 - 7(\frac{1}{2}) - 30 = 2(\frac{1}{4}) - \frac{7}{2} - 30 = \frac{1}{2} - 3.5 - 30 = -33$$ 4. Calculate $f(1)$: $$f(1) = 2(1)^2 - 7(1) - 30 = 2 - 7 - 30 = -35$$ --- **Problem 9:** Evaluate function values at given points. Assuming problem 21 function: $f(x) = x^3 - 4x^2 - 9x + 36$. 1. Calculate $f(2)$: $$f(2) = 2^3 - 4(2)^2 - 9(2) + 36 = 8 - 16 - 18 + 36 = 10$$ 2. Calculate $f(1)$: $$f(1) = 1^3 - 4(1)^2 - 9(1) + 36 = 1 - 4 - 9 + 36 = 24$$ 3. Calculate $f(3)$: $$f(3) = 27 - 4(9) - 27 + 36 = 27 - 36 - 27 + 36 = 0$$ 4. Calculate $f(-1)$: $$f(-1) = (-1)^3 - 4(-1)^2 - 9(-1) + 36 = -1 - 4 + 9 + 36 = 40$$ --- **Problem 21:** Evaluate function values at given points (same as problem 9 function). 1. Calculate $f(2)$: From above, $f(2) = 10$ 2. Calculate $f(1)$: From above, $f(1) = 24$ 3. Calculate $f(3)$: From above, $f(3) = 0$ 4. Calculate $f(-1)$: From above, $f(-1) = 40$ **Final answers:** - Problem 7: (a) $-8$, (b) $-21$, (c) $-33$, (d) $-35$ - Problem 9 and 21 (same function): (a) $10$, (b) $24$, (c) $0$, (d) $40$