PreCalculus Final Exam December 2024 PDF

**Name \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.** 1. Determine which relation is a function. In...

**Name \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.** 1. Determine which relation is a function. Input -2 0 1 2 -------- ---- ---- ---- ---- Output 0 -2 -3 -4 Input 3 3 2 0 -------- --- --- --- ---- Output 1 4 5 -3 A. B. Input 6 4 6 -1 -------- --- --- --- ---- Output 0 3 2 -2 Input 0 0 0 0 -------- --- --- --- --- Output 0 1 2 3 C. D. 2. For the function [\$f\\left( x \\right) = \\sqrt{x - 2}\$]{.math.inline} find f(-a). A. [\$\\sqrt{--a - 2}\$]{.math.inline} B. [\$\\sqrt{--a + 2}\$]{.math.inline} C. [\$\\sqrt{a + 2}\$]{.math.inline} D. [\$\\sqrt{a - 2}\$]{.math.inline} 3. Use the x-intercept method to find all real solutions of the equation: x^3^ + 10x^2^ +27x + 18 = 0. 4. Solve by any method: x^2^ -- 4x -- 5 = 0. 5. Solve by any method: -3x^2^ + 8x -- 4 = 0. 6. Solve by taking the square root of both sides: 3(x + 1)^2^ -- 36 = 0. 7. Solve: 7x = 2x^2^ + 1 8. Find all real solutions of the equation: [\$\\frac{x\^{2} - 7x - 8}{x - 8} = 0\$]{.math.inline}. 9. Find all real solutions of the equation: [\$\\sqrt\[3\]{4x - 7} + 14 = 11\$]{.math.inline}. 10. Find all real solutions of the equation: [\$\\left\| \\frac{5}{3}x + 6 \\right\| + 2 = 10\$]{.math.inline}. 11. Which of the following represents [3 ≤ *x* \ 12. Solve and express your answer in interval notation: [ − 10 ≤ 2*x* − 4 ≤ 0.]{.math.inline} 13. Which of the following is *not* a function given that x is an independent variable? 14. Determine the domain of the function: [\$h\\left( x \\right) = \\frac{4x}{x\\left( x\^{2} - 81 \\right)}.\$]{.math.inline} 15. Given: h(x) = [\$x\^{2} + \\sqrt{x + 11};\$]{.math.inline} determine the domain of the function: A. (-11, [∞]{.math.inline}) B. (11, [∞]{.math.inline}) C. (- [∞]{.math.inline}, -11\] D. \[-11, [∞]{.math.inline}) 16. Determine which graph defines a function. 17. Find all local maxima and minima for [*f*(*x*) =  − *x*^3^ + 3*x*^2^ + 9*x* − 9.]{.math.inline} 18. Determine the x-intercepts of the quadratic function [*f*(*x*)=  − 0.7(*x*+0.1)(*x*−0.4)]{.math.inline} and determine if its graph opens up or down. 19. Determine the x-intercepts and the vertex of the graph of the quadratic function [*f*(*x*) = *x*^2^ + 7*x* + 10]{.math.inline} 20. Find the rule of the function whose graph can be obtained by performing the following translation: 4 units right and 3 units up on the parent function[*f*(*x*) = *x*^2^]{.math.inline}. 21. The function f(x) is graphed below. C. x ≥ 0 22. Which equation is the vertex (transformation) form of f(x) = [ − 3*x*^2^ + 12*x* − 7 ]{.math.inline}? 23. [ ]{.math.inline}Given [*h*(*t*)= *t*^3^ + 3*t*]{.math.inline}, find [*h*(2+*t*)]{.math.inline}. A. [*t*^3^ − 12*t*^2^ + 51*t* − 76]{.math.inline} B. [*t*^3^ + 6*t*^2^ + 15*t* + 14]{.math.inline} C. [ − 64*t*^3^ − 12*t*]{.math.inline} D. [*t*^3^ + 3*t* + 14]{.math.inline} 24. For the function, find the average rate of change of f from 1 to x**:** (f(x) - f(1)/x - 1), x ≠ 1 f(x) = -2x A. 0 B. -3 C.  D. -2 25. Find the average rate of change for the function between the given values. A. -6 B. 6 C. 2 D. -2 26. Use the Remainder Theorem to find the remainder when f(x) is divided by x -- c. A. 27. Give the maximum number of zeros the polynomial function may have. Use Descartes Rule of Signs to determine how many positive and how many negative zeros it may have. A. 9; 3 or 1 positive zeros; 3 or 1 negative zeros B. 9; 2 or 0 positive zeros; 2 or 0 negative zeros C. 9; 2 or 0 positive zeros; 3 or 1 negative zeros D. 9; 3 or 1 positive zeros; 2 or 0 negative zeros 28. List the potential rational zeros of the polynomial function. Do not find the zeros. 29. Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. A. -3, 3; f(x) = (x - 3)(x + 3)( + 1) B. -1, -3, 1, 3; f(x) = (x - 1)(x + 1)(x - 3)(x + 3) C. -1, 1; f(x) = (x - 1)(x + 1)((x) with superscript (2) + 9) D. 1, 1; f(x) = (x -- 2)^2^ (x2 + 9) 30. Find the real zeros of f. If necessary, round to two decimal places. A. -5.23, -0.76, 3 B. -3, 0.38, 2.61 C. -3, 0.76, 5.23 D. -2.61, -0.38, 3 31. Find the intercepts of the function f(x). A. x-intercept: -3; y-intercept: -18 B. x-intercept: -2; y-intercept: -18 C. x-intercepts: -3, -2, 3; y-intercept: -18 D. x-intercepts: -3, 2, 3; y-intercept: -18 32. Find the real solutions of the equation. A. { 2, 3, 4} B. { -4, -3} C. {3, 4} D. { -4, -3, -2}