Mat120 Practice problems for Test I, Spring 2016 1. Use the quadratic formula to solve 2 6 = 3 2. Perform indicated operations and simplify ( 2)2 ( + 2)( 2) 10 2 5 3. Simplify 23 +2 4. Perform indicated operations 5. Simplify, express answers with positive exponents only 6. Change the expression 7 5 to radical form. 7. Write in simplest radical form: 326 11 8. Rationalize the denominator 7 2 1 3 2 3 3 8 4 5 3()2 9. Does the graph below represent a function? 10. The graph on the right represents y = f(x). Fill in the blanks. f(____) = 2 f(-5) = ____ x-intercept is (___,___) 11. Give the domain of () = 4 Answer in interval notation. 12. Given () = 4 2 , find and simplify the expression (2 + ) (2) 13. Write the equation for the graph on the right. y = _____________ 14. What is the equation for the graph on the right? y = ______________ 15. What is the domain of the graph on the right? Answer in interval notation. 16. Graph() = { 3 1 1 > 1 17. A plant can manufacture 50 tennis rackets per day for a total daily cost of $3855 and 60 tennis rackets per day for a total daily cost of $4245. Assume the cost and production are linearly related and find the total daily cost function for producing x rackets. Write answer in slope-intercept form. C = mx + b 18. Find the x and y-intercepts for the function () = ( 3)2 + 4. 19. What is the range of the function () = ( 3)2 + 4? Answer in interval notation. 20. Determine whether there is a maximum or a minimum value for () = 2 + 10 4 and find that value. 21. What is the minimum degree of the polynomial function in graph? Is the leading coefficient positive or negative? +2 22. Graph () = 22. Dot in the vertical and horizontal asymptotes and the x and y-intercepts. Also plot the point when x is 2. Vertical asymptote equation is_________ Horizontal asymptote equation is _________ x y 0 0 2 23. What is the degree and the x and y intercepts of the polynomial function () = ( 1)3 ( + 2)2 ? Degree is _______ x-intercepts: y-intercept: 24. What is the domain of the rational function () = 2 1 ? 2 9 Write your answer in interval notation. 25. Describe verbally the transformations of the graph of () = to obtain the graph of () = 2 1 26. Solve the equation 2 2 8 = 0. 27. Suppose $5000 is invested at 6% compounded weekly. How much money will be in the account in 5 years? Compound interest formulas are = and = (1 + ) 28. Rewrite = in equivalent logarithmic form. 29. Write 10 log in simpler form. . 30. Solve for x: log ( + 2) + log = log 15. The solution set is {__________}. 31. Graph the function = log 2 ( 1). Dot in the vertical asymptote. Show the x-intercept. 32. How many years (to two decimal places) will it take $2000 to grow to $2850 if it is invested at 5.5% compounded continuously? Compounded semiannually? Formulas are = and = (1 + ) 33. A company manufactures notebook computers. An analyst produced the price-demand function p(x) =2000 - 60x, domain 1 x 25, where p is the price per computer at which x thousand computers can be sold. The cost function is C(x) = 4000 + 500x thousand dollars. a. Write the company's revenue function. b. Find the value of x that will produce the maximum revenue. c. Write the company's profit function. d. Find the value of x that will produce the maximum profit. 34. A charter fishing company buys a new boat for $224,000 and assumes that it will have a trade-in value of $115,200 after 16 years. Find a linear model for the depreciated value of V of the boat in t years after it was purchased. This will be a function for V in terms of variable t. 35. At a price of $1.94 per bushel, the supply of corn is 9,800 million bushels and the demand is 9,300 million bushels. At the price of $1.82 per bushel, the supply is 9,400 million bushels and demand is 9,500 million bushels. You can verify that the price-demand function is p(x) = 0.0003x - 1 and the price-supply function is p(x) = -0.0006x + 7.52. Find the equilibrium point. Answers 1. 3 23 2. -4x+8 3. 4. 5. 5 +1 6 (3) 8 3 3 6 5 7 2 6. 3 7. 22 3 42 8. 21 7 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. Not a function, does not pass vertical line test (0) = 2, (5) = 3, (2,0) [4, ) 42 + 15 = | + 2| + 3 = + 5 [0, ) Graph of piecewise function = 39 + 1905 (0, -5), (5, 0), (1, 0) (, 4] Max. g(5) = 21 Degree 5, leading coefficient is negative 22. graph of rational function 23. degree 5, (1, 0), (-2, 0), (0, 4) 24. (, 3) (3,3) (3, ) 25. vertical stretch by factor of 2, down one unit 26. {-2, +2} 27. A=$6748.13. 28. log = 29. 30. x = 3 31. Graph of log function 32. compounded continuously t = 6.44 years, compounded biannually t = 6.53 years 33. a) R(x) = 2000x - 60x2 b) x = 16.67 thousand computers 34. V(t) = -6800t + 224,000 35. (9467, $1.84) c) P(x) = -60x2 + 1500x - 4000 d) x = 12.5 thousand computers