Part I: Multiple Choice Questions

Transcription

1 Name: Part I: Multiple Choice Questions. What is the slope of the line y=3 A) 0 B) -3 ) C) 3 D) Undefined. What is the slope of the line perpendicular to the line x + 4y = 3 A) -/ B) / ) C) - D) 3. Find the exact value of the following logarithmic expression: log 3 9 A) 3 B) 3) C) 9 D) 7 4. Write the logarithmic function log 5 a = b in exponential form. A) b 5 = a b B) a = 5 4) C) 5 b = a D) log( 5) + log( a ) = log( b) 5. What is the degree of the following polynomial: f ( x) = x( x ) ( x + 3) A) 7 B) 3 5) C) 5 D) 6 6. Which of the following correctly lists all of the zeros of the following 3 function: g ( x) = 4x( x 5) ( x + ) A) x= 0, x = -5, x = 3

2 B) x = 0, x = 5, x = - 6) C) x= -5, x = D) x= 5, x= - 7. Write the equation of a function that is finally graphed after the following transformations have been applied to the graph of y = x. () Shifted right 3 units. () Shifted down 4 units. A) y = ( x + 3) 4 B) y = ( x 3) 4 7) C) y = ( x + 4) 3 D) y = ( x 4) Identify the Domain of the following function A) The set of All Real Numbers { R} B) { x x 3} ; Equivalently ( 3 ) ( 3, ) C) { x x 3} ; Equivalently (,3 ) ( 3, ) D) { x x > 3} ; Equivalently ( 3, ) y = x 3, 8) 9. Find the solution set of 3x = 4 A) x = 4 B) x = -/3 9) C) x = D) x = or x = -/3 0. What is the product of + 3i and its conjugate. A) -5 B) 3 0) C) - D) 0. Given the graph provided, identify the intervals of increase on the graph. A) ( 4,4 ) B) ( 4, ) (0,) ) C) ( 0,3) (0,) D) (,0) (,4)

3 . For the graph above, choose the option below that best describes the set of all zeros for the function. A) x = 3 B) x = 0 ) C) x = - and x = D) x = -, x = 0, and x = 3. What is the correct way to represent { < x 5} A) (,5) x in interval notation. B) (,5 ] 3) C) [,5 ) D) [,5 ] 4. Find the exact value of the logarithmic expression ln( 3 ) e A) -3 B) 3 4) C) /3 D) 3 e 5. Find the exact value of the logarithmic expression log 4 + log 5 log A) 00 B) 7 5) C) 0 D) 6. Which statement best describes the asymptotes of the function 3x + 5 G( x) = x 6 A) There is a horizontal asymptote at y=0 B) There is a vertical asymptote at x=0 6) C) There is an oblique (slant) asymptote at y=3 D) There is a vertical asymptote at x=6 and a horizontal asymptote at y=3 E) None of the above. x 7. Which best describes the intercepts for the graph of g( x) = ( x )( x + ) A) x-intercepts at x = - and x = - B) x-intercepts at x= and x=- and y intercept at y=0 7) 3

4 C) x and y intercepts are both at (0, 0) D) y intercepts at y= and y=- E) No intercepts 8. Determine the maximum number of real zeros that the polynomial p ( x) = 6 x + 7x 4x + 3x + 9x 47 will have. A) 6 B) 8 8) C) 9 D) 5 9. Compute ( f g)() given that f ( x) = x and g( x) = x 3 A) 3 B) 9) C) 4 D) 0. Find the inverse of the following one-to-one function: A) y = x B) y = x C) y = x D) y = + x f ( x) = x 0). Identify the vertex of the following quadratic: h( x) = x x 3 A) (, 3) B) (-, 0) ) C) (, -4) D) (, -3) 4. Choose the option below that best describes the function y = x x A) The function is even B) The function is odd ) C) The function is neither even nor odd. D) The function does not pass the vertical line test. 3. Which option describes a circle with a radius of 4 and a center at (, -3). A) ( x + ) + ( y 3) = 6 B) ( x ) + ( y + 3) = 6 3) 4

5 C) x y 3 =4 D) x y 3 =4 E) None of the above. 4. Write the equation of a line that goes through the points (, -6) and (-, 3) A) y = -3x + 8 B) y = -9x - 6 4) C) y = 3x D) y = -3x E) None of the above. Part II: Short Answer Questions (No Calculator) Name: Directions: For each of the following short answer questions show any work that leads you to your final answer. Partial credit will be awarded for correct steps toward the final solution. Box and clearly label your final answer.. (3 points). Solve the equation: t =. Be sure to check for extraneous solutions. Answer:. (4 points). Given the equation of a circle, x y x 4y 4=0 a) Find the center and radius of the circle. Center: Radius: b) (3 points). Find the equation of the line (in slope intercept form) that passes through the center of the circle and the point (, ) 5

6 Answer: 3. Given f x =x x 4 a) (3 points). Find the difference quotient f x h f x h and simplify. b) ( points). If f x =, what are the values of x? Answer: 4. (5 points). For the following function, state the transformations and sketch the graph (You may change the scale on the graph provided if necessary). Label at least 3 important points on your graph. g x = x 3 Transformations:

7 5. (6 points). Graph the following piecewise defined function. You may x 4 if - x change the scale on the grid provided if necessary. -3 if x 6 g x = { } {} function f x =x x 6. Answer the following questions about the a) ( point). Is the point (-, ) on the graph of f (answer yes or no)? b) ( points). If x = -, what is f(x)? c) ( points). List the x-intercepts if any of the graph: d) ( point). List the y-intercepts if any of the graph: 7. Answer the questions given the rational function g x = x x 4 a) ( point). Write g(x) in factored form and reduce if possible. g(x) = b) (3 points). Write the equation of all asymptotes present in the graph of g(x) Vertical Asymptotes: Horizontal or Oblique (slant) Asymptotes: c) ( points). State the Domain of g(x): 8. a) (4 points). Graph f x =log x and g x = x on the same coordinate grid and clearly label which is which. Also label at least 3 important points on each graph. (You may change the scale on the coordinate grid if necessary). 7

8 b) ( point). Are these two functions inverses (yes or no)? 9. (3 points each). Solve the following equations: a) x =5 x Answer: b) log 3 x = log 3 Answer: Name: Part III: Short Answer Questions: Calculator Allowed Directions: You may use a graphing calculator on this part of the exam. On some problems you will still be required to show your work. 8

9 . Iodine 3 is a radioactive material that decays according to the function A t = A 0 e 0.087t, where A 0 is the initial amount present and A is the amount present at time t (in days). Assume that a scientist has a sample of 00 grams of iodine 3. a) ( points). What is the decay rate of Iodine 3? Answer: b) ( points). Graph the function using a graphing utility and provide a rough sketch below. Provide an appropriate scale and clear labels. (You may change the scale on the coordinate grid if necessary). c) ( points). How much iodine 3 is left after 9 days? Answer: d) ( points). When will 70 grams of iodine 3 be left? Answer:. Given the function: f x =x 4 9x 3 x x 30 a) ( points). Draw a complete graph of f(x). (Change the scale on the coordinate grid as necessary). 9

10 b) ( points). The rational zeros of f occur at: c) ( point each). Find all local maximum and minimum values of f(x). If there are none, write none. Max Values: Min Values: d) (3 points). Find the remaining complex zeros (show all of your work!). Leave your answers in reduced radical form. Complex Zeros: 3. The marketing manager at Levi-Strauss wishes to find a function that relates the demand D for men s jeans and p, the price of the jeans. The following data were obtained based on a price history of the jeans. Price ($/Pair), p Demand (Pairs of Jeans Sold Per Day), D a) ( point). Does the relation defined by the set of ordered pairs (p, D) represent a function (yes or no)? b) ( point). Draw a scatter diagram of the data. (You may change the scale as needed). 0

11 c) ( point). Use a graphing utility to find the line of best fit that models the relation between price and quantity demanded. Round all values in the line of best fit to 3 decimal places. y = d) ( point). How many jeans will be demanded if the price is $8 a pair? Answer: 4. (3 points). Use your calculator to solve the following equation for x: 4 x 99 x 8=0 (Round your answer(s) to 3 decimal places). Answer(s): 5. ( points). Evaluate the following (round to 4 decimal places): log 3 5 Answer: 6. (3 points). Write the equation of one possible polynomial which has x- intercepts at x= -3, x= 4, x= -, and x= 0. Also, the degree of the polynomial is 0 and it is known that the graph crosses the x-axis at x = -3 and touches the x-axis at x = 4 and x=0. Answer: 7. (3 points). Write the equation of a quadratic which has a vertex at (6-4) and goes through the point ( -5) Answer: