Need help on Algebra..any help is appreciated. Answer key is attached

There are 30 problems. Problems #112 are Multiple Choice. Problems #13~2l are Short Answer. (Work not required to be shown) Problems #2230 are Short Answer with work required to be shown. MULTIPLE CHOICE 1. Determine the domain and range of the piecewise function. A. Domain [~3/2, 1/2]; Range [1, 0] B. Domain {1, I]; Range [1, 3] C. Domain {-1, 3]; Range [#2, 2] D. Domain {2, 2}; Range {1, 3] 2. Solve: v74x=x+3 A No solution B. 8, 2 C. -2 D 1/2 Page 1 ofll 3. Determine the interval(s) on which the function is decreasing. 3. A. ('3.6, 0) and (6.7, m) B. (m, w~33) and (4, ) C. (1, 3) D. (2, 4) 4. Determine whether the graph of y = Ixf - 2 is symmetric with respect to the origin, the xaxis, or the yaxis. 4 ._. A. symmetric with respect to the xaxis only B. symmetric with respect to the y-axis only C. symmetric with respect to the origin only D. not symmetric with respect to the xaxis, not symmetric with respect to the yards, and not symmetric with respect to the origin 5. Solve, and express the answer in interval notation: I 7 5x I S 8. 5. A. [w 1/5, 00) B. . [- 1/5, 3] C. (-m, 1/5] 13- (, -1/5] U [3, 0) PageZofll College Algebra - 6. Which of the following represents the graph of 4x - 7): = 28 '2 6. A. B. PageSofll College Algebra - 7. Write a slopeintercept equation for a line parallel to the line x + 3y = 8 which passes through the point (m 4, 5). 7. A. y=3x-7 B. y =%x+5 1 11 C. = x+ y 3 3 D. = l x + 5 3 8. Which of the following best describes the graph? 8- .______ A. It is not the graph of a function. B. It is the graph of an absolute value relation. C. It is the graph of a function and it is onetoone. D. It is the graph of a function but not one-to-one. Page 4 of 11 9. Express as a single logarithm: log x ~ 3 log y + log 1 9. 3 A. log [Jr+1] y B. log(x3y+1) C. 10g [36?] y D' 10g[3yx+1] 10. Which of the functions corresponds to thc graph? 10. Page 5 of 1] couege Algebra - 11. Suppose that for a function f , the equation f (x) = 0 has exactly one rea1~number solution. Which of the following statements MUST be true? f is a linear function. f (x) 2 O for all x in the domain off. f has exactly one real-number zero. f is an invertible functiOn. POP\"? 11. 12. The graph of y a f (x) is shown at the left and the graph of y = g(x) is shown at the right. (No formulas are given.) What is the relationship between g(x) and f (x)? 12. y = 5'06) 30:) =fx 2) 3 get) =f(x + 2) 3 g(x)=f(X3)2 306) =f(x+ 3) 2 F709\"? Page 6 ofll College Algebra - SHORT ANSWER: l3. Multiply and simplify: (3 + 2i)(1 61'). Write the answer in the form a + bi, where a and b are real numbers. Answer: . . . . x+4 14. Solve, and write the answer in interval notation: E 2 0 . Answer: x 15. A can of soda at 74 F. is placed in a refrigerator that maintains a constant temperature of 35 F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by m) = 35 + 39 e '0'058' Find the temperature of the soda 22 minutes after it is placed in the refrigerator. (Round to the nearest degree.) Answer: W 16. Find the value of the logarithm: log6 [56]. AnSWer: W 17. Solve: 43x8 =16 . Answer: M 18. Suppose $6,700 is invested in an account at an annual interest rate of 5.5% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer: WM 19. Let f(x) =x2 +14x+ 52. (3) Find the vertex. Answer: (b) State the range of the function. Answer: (c) On what interval is the function decreasing? Answer: Page'iofll College Algebra - 20. Consider the polynomial P(x), shown in both standard form and factored form. P(x) = ;~x4 +313 ~31? %x+3 = -(x+2)(x~1)(x~3)(x4) (a) Web sketch illustrates the end behavior of the polynomial function? A. N B. M C. W 7D. m] Answer: \" (b) State the yintercept. Answer: (c) State the zeros of the function. Answer: ((1) State which graph below is the graph of P(x). Answer: GRAPH A GRAPH B Page 8 of 11 21. Let f(x):2h{. (a) State the domain. 0}) State the horizontal asymptote. (c) State the vertical asymptote(s}. ((1) Which of the following represents the graph of f (x) = GRAPH A. GRAPH C. Z-x 3+x ? GRAPH B. GRAPH D. Answer: Answer: Answer: Answer: Pagerfll College Algebra - SHORT ANSWER, With work required to be shown, as indicated. 22.Let f(x)=x+l and g(x)=\\/x+5. (a) Find [1}4) . Show work. 3 (b) Find the domain of the quotient function "1:. Explain. 5' 23. Points (5, i) and (9, 7) are endpoints of the diameter of a circle. (a) What is the length of the diameter? Give the exact answer, simplied as much as possible. Show work. (b) What is the center point C of the circle? (0) Given the point C you found in pant (b), state the point symmetric to C about the y-axis. M 24. Find the equation for a Iine which passes through the points (- 1, 8) and (4, 3). Write the equation in slopeintercept form. Show work. M 25. A salesperson earns a base salary of $1,475 per month and a commission of 7.4% on the amount of sales. If the salesperson has a paycheck of $3,606.20 for one month, what was the amount of sales for the month? Show work. M 26.Letf(x)=5x2+8 and g(x)=x3. (3) Find the composite function (f o g)(x) and simplify. Show work. (b) Find ( f o g)(2). Show work. "W 27. Find the exact solutions and simplify as much as possible: 2x2 + 11 = 10x. Show work. M 28. Given the function f (x) = 7 mx , nd a formula for the inverse function. Show Work. W Page IOofll coucge Algebra - 29. The fuel efciency F for a particular car is given by F(x) = 40.018 x2 + 1.656 x + 4.4 where x is the speed of the car in miles per hour (mph) and F(x) is the corresponding fuel efciency in miles per gallon (mpg). (21) What is the fuel efciency if the car's speed is 20 mph? (b) What speed will yield the maximum fuel efciency? Show work. % x+7 20 + x+2 x24 30. Solve: = 0 . Show work. Page 11 ofll aSL/JEK Sheef This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. Record your answers and work in this document. There are 30 problems. Problems #112 are multiple choice. Record your choice for each problem. Problems #13'21 are short answer. Record your answer for each problem. Problems #22-30 are short answer with work required. When requested, show all work and write all answers in the spaces allotted on the following pages. You may type your work using plain- text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages. MULTIPLE CHOICE. Record your answer choices. 1. 7. 2. 8. 3. 9. 4. 10. 5. 11. 6. 12. SHORT ANSWER. Record your answers below. 13. 14. 15. 16. 17. 18. 19. (a) (b) (C) 20. (a) (b) (C) (d) 21- (a) (b) (C) (d) SHORT ANSWER with Work Shown. Record your answers and work. Solution Answers: (a) (b) Work/for part (a) and explanation for part (b): Answers: (a) (b) (C) Work for part (a): 23 Answer: Work: Answer: Work: Answers: (a) 0)) Work for part (a) and for part (b): \f\f