Algebra homework
MAT111A - College Algebra Quiz 3 (20 Questions) The following questions were adapted from Larson, R.(2018). College Algebra (10th 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. Scoring: 2 points each 1. Give the domain and range for this relation. Describe whether the relation is a function or not. {(3, -2), (5, -2), (7, 1), (4, 9)} 2. Using the coordinate template below, draw a graph with the square root functions, f and g, in the same rectangular coordinate system. Use the integer values of x given to the right of each function to obtain ordered pairs. Once the functions are graphed, describe how the graph of g is related to the graph of f. f(x) = √? (x = 0, 1, 4, 9) g(x) = √? + 2 (x = -2, -1, 2, 7) 2 4 -2 -4 -6 6 x 2 4 -2 -4 6 -6 8 10 -8 -10 8 10 -8 -10 y 3. Evaluate the graph below and determine if y is a function of x. Describe the method used for this determination. 4. Use the graph below to determine: a. the function’s domain b. the function’s range c. the x-intercepts, if any d. the y-intercept, if any e. the function’s values ?(−4) and ?(3) 5. Use the graph below to determine: a. the intervals on which the function is increasing, if any b. the intervals on which the function is decreasing, if any c. the intervals on which the function is constant, if any 6. Examine the graph below, use possible symmetry to determine whether the graph is the graph of an even function, an odd function, or a function that is neither even nor odd. 7. Use the graph of f below to determine each of the following. Where applicable, use interval notation. a. the domain of f b. the range of f c. f(0) d. intervals on which f is increasing e. intervals on which f is decreasing f. values of x for which ?(?) ≤ 0 g. any relative maxima and the numbers at which they occur h. the value of x for which f(x) = 4 i. Is f(-1) positive or negative? 8. The function ?(?) = −0.002?2 + 0.15? + 22.86 models percent body fat, p(x), where x is the number of years a person’s age exceeds 25. Use the graphs below to determine whether this model describes percent body fat in women or in men. 9. Find the slope of the line passing through the pair of points (4, -2) and (3, -2). Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. 10. Use the conditions of a line, Slope = -2/3, passed through (6, -2), to write an equation for the line in point-slope form and slope-intercept form. 11. Give the slope and y-intercept of the line whose equation is ?(?) = 2 5 ? + 6. Then graph the linear function. Use the coordinate template below draw to graph ?(?). Slope: y-intercept: 2 4 -2 -4 -6 6 x 2 4 -2 -4 6 -6 8 10 -8 -10 8 10 -8 -10 y 12. Find the value of y if the line through the two given points is to have the indicated slope. (3, ?) ??? (1,4), ? = −3 13. Write an equation for line L in point-slope form and slope-intercept form. 14. Find the average rate of change of the function ?(?) = ?2 − 2? from ?1 = 3 to ?2 = 6. 15. Write an equation in slope-intercept form of a linear function f whose graph satisfies the following conditions. The graph of f is perpendicular to the line whose equation is 3? − 2? − 4 = 0 and has the same y-intercept as this line. 16. The function ?(?) = 1.1?3 − 35?2 + 264? + 557 models the number of discharges, f(x), under “don’t ask, don’t tell” x years after 1994. Use this model and its graph below on the domain [ 0, 12 ]. Find the slope of the secant line, rounded to the nearest whole number, from ?1 = 0 to ?2 = 4. 17. Use the graph of y = f(x) to graph the function ?(?) = ?(−?) + 3. Using the coordinate template below draw the graph of ?(?). x 1 2 3 4 -1 -2 -3 -4 1 2 3 4 -1 -2 -3 -4 5 -5 5 -5 18. Use the graph of y = f(x) to graph the function ?(?) = 2?(? + 2) + 1 . Use the coordinate template below to draw the graph of ?(?). x 1 2 3 4 -1 -2 -3 -4 1 2 3 4 -1 -2 -3 -4 5 -5 5 -5 19. Graph the standard quadratic function, ?(?) = ?2. Then use transformations of this graph to graph the function ℎ(?) = −2(? + 2)2 + 1. Use the coordinate template below to draw the graph of ℎ(?). x 1 2 3 4 -1 -2 -3 -4 1 2 3 4 -1 -2 -3 -4 5 -5 5 -5 20. The function ?(?) = 3.1√? + 19 models the median height, f(x), in inches, of girls who are x months of age. The graph of f is shown below. a. Describe how the graph can be obtained using transformations of the square root function ?(?) = √?. b. Use the model to find the average rate of change, in inches per month, between birth and 10 months. Round to the nearest tenth. c. Use the model to find the average rate of change, in inches per month, between 50 and 60 months. Round to the nearest tenth. How does this compare with your answer in part (b)? How is this difference shown by the graph? MAT111A - College Algebra Homework Problems 3 (20 Questions) The following questions were adapted from Larson, R.(2018). College Algebra (10th 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. Scoring: 1 point each 1. Give the domain and range for this relation. Describe whether the relation is a function or not. {(4, 5), (6, 7), (8, 8)} 2. Using the coordinate template below, draw a graph with the square root functions, f and g, in the same rectangular coordinate system. Use the integer values of x given to the right of each function to obtain ordered pairs. Once the functions are graphed, describe how the graph of g is related to the graph of f. f(x) = √? (x = 0, 1, 4, 9) g(x) = √? + 2 (x = 0, 1, 4, 9) 2 4 -2 -4 -6 6 x 2 4 -2 -4 6 -6 8 10 -8 -10 8 10 -8 -10 y 3. Evaluate the graph for Exercise 12 on Page 194 and determine if y is a function of x. Describe the method used for this determination. 4. Use the graph for Exercise 10 on Page 194 to determine: a. the function’s domain b. the function’s range c. the x-intercepts, if any d. the y-intercept, if any e. the function’s values ?(−1) and ?(2) 5. Use the graph for Exercise 37 on Page 195 to determine: a. the intervals on which the function is increasing, if any b. the intervals on which the function is decreasing, if any c. the intervals on which the function is constant, if any 6. Examine the graph for Exercise 11 on page 194, use possible symmetry to determine whether the graph is the graph of an even function, an odd function, or a function that is neither even nor odd. 7. Use the graph for Exercise 34 on Page 195 displaying the function f to determine each of the following. Where applicable, use interval notation. a. the domain of f b. the range of f c. the x-intercepts d. the y-intercept e. intervals on which f is increasing f. intervals on which f is decreasing g. intervals on which f is constant h. the x-coordinate at which f has a relative minimum i. the y-coordinate at which f has a relative minimum j. f(-1) k