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MAT111A - College Algebra Homework Problems 3 (20 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. Scoring: 1 point each Give the domain and range for this relation. Describe whether the relation is a function or not. {(4, 5), (6, 7), (8, 8)} 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) 2 4 -2 -4 -6 6 x 2 4 -2 -4 6 -6 8 10 -8 -10 8 10 -8 -10 y 2 4 -2 -4 -6 6 x 2 4 -2 -4 6 -6 8 10 -8 -10 8 10 -8 -10 y g(x) = (x = 0, 1, 4, 9) Evaluate the graph for Exercise 62 on Page 231 and determine if y is a function of x. Describe the method used for this determination. Use the graph for Exercise 79 on Page 231 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 and Use the graph for Exercise 2 on Page 249 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 Examine the graph for Exercise 35 on page 250, 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. Use the graph for Exercise 49 on Page 250 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 number at which f has a relative minimum i. the relative minimum of f j. f(-3) k. the values of x for which f(x) = -2 l. is f even, odd, or neither? With aging, body fat increases and muscle mass declines. The line graphs for Exercises 99-106 on Page 253 show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to answer the following: State the intervals on which the graph giving the percent body fat in women is increasing and decreasing. For what age does the percent body fat in women reach a maximum? What is the percent body fat for that age? Find the slope of the line passing through the pair of points (-2, 1) and (2, 2). Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. Use the conditions of a line, Slope = -2, passed through (0, -3), to write an equation for the line in point-slope form and slope-intercept form. Give the slope and y-intercept of the line whose equation is . Then graph the linear function. Use the coordinate template below to draw the graph of . Slope: y-intercept: x 1 2 3 4 -1 -2 -3 -4 1 2 3 4 -1 -2 -3 -4 5 -5 5 -5 x 1 2 3 4 -1 -2 -3 -4 1 2 3 4 -1 -2 -3 -4 5 -5 5 -5 Using the graph below, list the slopes m1, m2, m3, and m4 in order of decreasing size. Largest Slope: Second Largest: Second Smallest: Smallest Slope: Write an equation for line L in point-slope form and slope-intercept form. Find the average rate of change of the function from . Write an equation in slope-intercept form of a linear function f whose graph satisfies the following conditions. The graph of f passes through (-6, 4) and is perpendicular to the line that has an x-intercept of 2 and a y-intercept of -4. The bar graph below shows that as costs changed over the decades, Americans devoted less of their budget to groceries and more to health care. Find a linear function in slope-intercept form that models the two descriptions below. Each function should model the percentage of total spending, p(x), by Americans x years after 1950. In 1950, Americans spent 22% of their budget on food. This has decreased at an average rate of approximately 0.25% per year since then. Use the graph of y = f(x) to graph the function . 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 x 1 2 3 4 -1 -2 -3 -4 1 2 3 4 -1 -2 -3 -4 5 -5 5 -5 Use the graph of y = f(x) to graph the function . 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 x 1 2 3 4 -1 -2 -3 -4 1 2 3 4 -1 -2 -3 -4 5 -5 5 -5 Graph the standard quadratic function, . Then use transformations of this graph to graph the function . 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 x 1 2 3 4 -1 -2 -3 -4 1 2 3 4 -1 -2 -3 -4 5 -5 5 -5 The function models the median height, f(x), in inches, of boys 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?