MAT111A - College Algebra Homework Problems 4 (15 Questions) The following questions were adapted from Blitzer, R.(2018). College Algebra (7th ed) . NOTE: Be sure to show your work for the solution to each question. Partial credit may be given, even if the final answer is not correct, as long at the proper concepts are being depicted. 1. (1 Point) From the graph of the quadratic function shown below, select the function's equation from the available options. a. f ( x )=x 2 +2 x +1 b. g ( x ) =x2 2 x +1 c. h ( x )=x 21 d. j ( x )=x 21 2. (1 Point) Find the coordinates of the vertex for the parabola defined by the quadratic function f ( x )=2 x 28 x+ 3 The vertex is at x = _____ and y = _____ x1 3. (2 Points) For the quadratic function f ( x )=4 a. Use the vertex and intercepts to sketch the graph of this quadratic function. b. Give the equation of the parabola's axis of symmetry. c. Use the graph to determine the function's domain and range. Use the coordinate template below to draw the graph y 10 8 6 4 2 -10 -8 -6 -4 -2 2 -2 -4 -6 -8 -10 4 6 8 10 x 4. (2 Points) A ball is thrown upward and outward from a height of 6 feet. The height of the ball, f(x), 2 f ( x )=0.8 x +2.4 x+6 , where x is the ball's horizontal distance, in in feet, can be modeled by feet, from where it was thrown. a. What is the maximum height of the ball and how far from where it was thrown does this occur? b. How far does the ball travel horizontally before hitting the ground? Round to the nearest tenth of foot. c. Graph the function that models the ball's parabolic path. Use the coordinate template below to draw the graph. y 10 8 6 4 2 -10 -8 -6 -4 -2 2 -2 -4 -6 -8 -10 4 6 8 10 x 5. (1 Point) Which function is a polynomial function with degree 5? 2 3 a. f ( x )=5 x + 6 x b. f ( x )=7 x 22 x5 +1 c. f ( x )=7 x 5 +2 x 2 + d. f ( x )=x +2 x +5 1 x 2 6. (1 Point) Using the Leading Coefficient Test, what is the end behavior of the graph of the polynomial function ( x )=5 x 4 +7 x 2x +9 ? a. The graph of f(x) falls the left and rises to the right b. The graph of f(x) falls the left and falls to the right c. The graph of f(x) rises the left and rises to the right d. The graph of f(x) rises the left and falls to the right 7. (2 Points) For the polynomial function f ( x )=x 4 +4 x2 a. Use the Leading Coefficient Test to determine the graph's end behavior. b. Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. c. Find the y-intercept. d. Determine whether the graph has y-axis symmetry, origin symmetry, or neither. e. If necessary, find a few additional points and graph the function. Use the maximum number of turning points to check whether it is drawn correctly. Use the coordinate template below to draw the graph of y f (x) . 10 8 6 4 2 -10 -8 -6 -4 -2 2 -2 -4 -6 -8 -10 4 6 8 10 x 8. (2 Points) Refer to the graphs and description for Application Exercise #73 on Page 379. Then provide the following information a. Find and interpret f(40). How would this information be displayed as a point on the graph of f? b. Does f(40) overestimate or underestimate the actual data shown by the bar graph? By how much? c. Use the Leading Coefficient Test to determine the end behavior to the right for the graph of f . Will this function be useful in modeling the world tiger population if conservation efforts to save wild tigers fail? Explain your answer. 9. (1 Point) Describe the steps for dividing the following two polynomials using long division. State the quotient, q(x), and the remainder, r(x). x 4 + 2 x 34 x 25 x6 x 2+ x 2 10. (1 Point) Describe the steps for dividing the following two polynomials using synthetic division. State the quotient, q(x), and the remainder, r(x). (x 25 x5 x3 + x 4 )(5+ x) 11. (1 Point) Refer to the diagram of the rectangular box for Exercise #52 on Page 393. a. Use synthetic division to show that 2 is a solution of the polynomial equation (show your work) 2 h3 +14 h272 b. Use the solution from part (a) to solve this problem. The width of a rectangular box is twice the height and the length is 7 inches more than the height. If the volume is 72 cubic inches, find the dimensions of the box. 12. (1 Point) Refer to the graph of the rational function for Exercises 15-20 on page 427 and complete the following statements. a. As x _____ b. As x 1-, f(x) _____ c. As x -2+, d. As x -2-,f(x) _____ e. As x _____ f. -,f(x) _____ As x 1+, f(x) , f(x) f(x) _____ 13. (1 Point) Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the rational function g (x )= x3 2 x 9 . Describe the steps to complete this and provide your answers. Vertical Asymptotes: Holes at x = 14. (1 Point) Find the horizontal asymptote, if there is one, of the graph of the rational function g (x )= 12 x 2 3 x 2+1 . Describe the steps to complete this and provide your answers. Horizontal Asymptote: 15. (2 Points) Use transformations of ( x )= 1 ( x +2)2 f ( x )= 1 x or f ( x )= 1 2 x to graph the rational function . Use the coordinate template below to draw the graph of y g (x ) . 10 8 6 4 2 -10 -8 -6 -4 -2 2 -2 -4 -6 -8 -10 4 6 8 10 x