Test 3 review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Approximate the coordinates of each turning point by graphing f(x) in the standard viewing rectangle. Round to the nearest hundredth, if necessary. 1) f(x) = 0.1x4-0.55x3 + 0.3x2-0.15x - 2 Solve the inequality. 2) (x - 3)(x + 4) < 0 Identify any vertical asymptotes in the graph. 3) The given graph represents a translation of the graph of y = x2. Write the equation of the graph. 4) 1
The graph of a polynomial is given. Identify the degree of the polynomial, the turning points, and any x-intercepts. Also estimate any local maxima or minima and any absolute maxima or minima. 5) Use the given graph of f(x) = ax2 + bx + c to solve the specified inequality. 6) f(x) < 0 Solve the problem. 7) If the average cost per unit C(x) to produce x units of plywood is given by C(x) = 1200, what is the unit cost for x + 40 50 units? 8) The table shows the number of cases of a certain infectious disease over a 25-year period in a certain city. Year 1965 1970 1975 1980 1985 1990 Number of Cases 100 85 60 26 33 48 Determine whether a linear, quadratic, cubic, or quartic polynomial best fits this data. 9) A rock falls from a tower that is 272 feet high. As it is falling, its height is given by the formula h = 272-16t2. How many seconds (in tenths) will it take for the rock to hit the ground (h = 0)? 10) Assume that the elevation E, in feet, of a sag in a proposed route is given by E(x) = 0.000036x2-0.28x + 1200, where x represents the horizontal distance in feet along the proposed route and 0 x 5000. For what x-values is the elevation 1050 feet or more? Round your answer to the nearest foot. 2
11) A rock is thrown vertically upward from the surface of the moon at a velocity of 36 m/sec. The graph shows the height y of the rock, in meters, after x seconds. Estimate and interpret the turning point. Solve the equation. 12) x - 5 x + 3 = 4 Graph the function. 13) f(x) = (3x - 2)(x + 2)(x - 1) State the end behavior of the graph of f. 14) f(x) = 6x3 Determine the vertex of the graph of f. 15) f(x) = -2x2 + 20x - 47 Solve the quadratic equation. 16) 2x2 + 8x + 5 = 0 3
Use the graph of f to determine the intervals where f is increasing and where f is decreasing. 17) Use the given graph to find the x-intercepts. 18) Find any vertical asymptotes. 19) f(x) = x - 1 x2 + 6 Use the given graph of the quadratic function f to write its formula as f(x) = a(x - h)2 + k. 20) 4
Sketch the graph of the rational function. 2x 21) f(x) = (x - 1)(x - 5) Find f(x) = a(x - h)2 + k so that f models the data exactly. 22) x -4-3 -2-1 0 y 7.5 7 7.5 9 11.5 Use the graph of the quadratic function to determine the sign of the leading coefficient, the vertex, and the equation of the axis of symmetry. 23) 5
The graph of f(x) = ax2 + bx + c is given in the figure. Solve the equation ax2 + bx + c = 0. 24) Determine whether the given equation is a rational function. 25) f(x) = x 4 + 6x - 2 2x1/2 Find an equation that shifts the graph of f by the indicated amounts. 26) f(x) = x4; right 8 units, up 4 units The graph of f(x) = ax2 + bx + c is given in the figure. Determine whether the discriminant is positive, negative, or zero. 27) Find the horizontal asymptote of the given function. 28) h(x) = 10x 2 5x2-7 6
Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. 29) y = - 1 2 f(x) Answer the question. 30) How can the graph of f(x) = -10x2 + 6 be obtained from the graph of y = x2? Write the equation as f(x) = a(x - h)2 + k. Identify the vertex. 31) f(x) = x2 + 3x + 1 Identify any horizontal asymptotes in the graph. 32) Use regression to find a quadratic function that best fits the data. Give results to the nearest hundredth. 33) x 2 34 79 110 f(x) 1024 2345 2267 984 Find any slant asymptotes of the graph of f. 34) f(x) = x 2 + 9x - 7 x - 4 7
In the table, Y1 is a rational function. Give a possible equation for a horizontal asymptote. 35) X Y1 50 3.8425 100 3.8457 150 3.8684 200 3.8844 250 3.9128 300 3.9533 350 3.9923 X = 50 The data table has been generated by a linear, quadratic, or cubic function f. All zeros of f are real numbers located in the interval [-3, 3]. By making a line graph of the data, conjecture the degree of f. 36) x -3-2 -1 0 1 2 3 f(x) -12 0-2 -6 0 28 90 Find the domain of f. 37) f(x) = x - 1 x2-4 The graph of f(x) = ax2 + bx + c is given in the figure. State whether a > 0 or a < 0. 38) 8
Identify f as being linear, quadratic, or neither. If f is quadratic, identify the leading coefficient. 7 39) f(x) = 5x2 + 2 Use the given table for f(x) = ax2 + bx + c to solve the inequality f(x) < 0. 40) x -12-8 -4 0 4 8 12 f(x) 80 0-48 -64-48 0 80 Identify the interval where f is increasing or decreasing, as indicated. Express your answer in interval notation. 41) f(x) = -5x2 + 10x - 7; decreasing Two functions f and g are related by the given equation. Use the numerical representation of f to make a numerical representation of g. 42) g(x) = f(x + 1) x 6 7 8 9 10 f(x) 15 17 19 21 23 9