Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for College Algebra (MindTap Course List)
36EEach equation defines a one-to-one function f. Determine f-1 and verify that ff-1 and f-1f are both the identity function. fx=3xEach equation defines a one-to-one function f. Determine f-1 and verify that ff-1 and f-1f are both the identity function. fx=13xEach equation defines a one-to-one function f. Determine f-1 and verify that ff-1 and f-1f are both the identity function. fx=3x+2Each equation defines a one-to-one function f. Determine f-1 and verify that ff-1 and f-1f are both the identity function. fx=2x-5Each equation defines a one-to-one function f. Determine f-1 and verify that ff-1 and f-1f are both the identity function. fx=x3+242EEach equation defines a one-to-one function f. Determine f-1 and verify that ff-1 and f-1f are both the identity function. fx=x5Each equation defines a one-to-one function f. Determine f-1 and verify that ff-1 and f-1f are both the identity function. fx=x5+4Each equation defines a one-to-one function f. Determine f-1 and verify that ff-1 and f-1f are both the identity function. fx=1x+346EEach equation defines a one-to-one function f. Determine f-1 and verify that ff-1 and f-1f are both the identity function. fx=12x48EFind the inverse of each one-to-one function and graph both the function and its inverse on the same set of coordinate axes. y=5x50EFind the inverse of each one-to-one function and graph both the function and its inverse on the same set of coordinate axes. y=2x-452E53E54E55E56EFind the inverse of each one-to-one function and graph both the function and its inverse on the same set of coordinate axes. fx=x-43Find the inverse of each one-to-one function and graph both the function and its inverse on the same set of coordinate axes. fx=x+3359E60E61E62E63EFind the inverse of each one-to-one function and graph both the function and its inverse on the same set of coordinate axes. fx=x-1x65E66E67E68E69E70E71E72E73E74E75E76EFind the domain and the range of f.Find the range by finding the domain of f-1. fx=1x-2Find the domain and the range of f.Find the range by finding the domain of f-1. fx=3x-1279EApplications Cell phone bills A phone company charges 11 per month plus a nickel per call. a. Find a rational function that expresses the average cost fx of a call in a month when x calls were made. b. To the nearest tenth of a cent, find the average cost of a call in a month when 68 calls were made. c. Find the inverse of the function found in a part a to find a formula that gives the number of calls f-1x that can be made for an average cost x. d. How many calls need to be made for an average cost of 15c per call?81E82E83E84E85E86E87E88E89E90E91E92E93E94E95E96E1E2E3E4E5E6E7EExercises Graph each function. Use the graph to identify the domain and range of each function. fx=-x-49E10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29E30E31E32E33E34E35E36E37E38E39E40E41E42E43E44E45E46E47E48E49E50E51E52E53E54E55E56E57E58E59E60E61E62E63E64E65E66E67E68E69E70E71E72E73EFind two functions fand g such that the composition fg=h expresses the given correspondence. Several answers are possible. hx=x+6375E76E77E78E79E80E81EEach equation defines a one-to-one function. Find f-1 and verify that ff-1 and f-1f are the identity function. y=5x-883E84E85E86EEach equation defines a one-to-one function. Find f-1 and verify that ff-1 and f-1f are the identity function. y=x1-x88E89E90EGraph each function by plotting points. fx=2x+1+2Graph each function by plotting points. fx=-2x3-4Use the graph of the function shown to determine the following. Domain and rangeUse the graph of the function shown to determine the following. f15CT6CTUse transformations to graph each function. fx=-x-13+3Use transformations to graph each function. fx=-12x+5-2Use transformations to graph each function. fx=2x-63-110CT11CTUse the graph to determine any local maxima or minima.Use the piecewise-defined function shown to find each value. fx=2xifx03-xif0x2xifx2 f32Use the piecewise-defined function shown to find each value. fx=2xifx03-xif0x2xifx2 f515CT16CT17CT18CT19CT20CT21CTLet fx=2x2-5x+1and gx=5x+1. Find each function value. fg-123CT24CT25CT26CT27CT28CT29CT30CT1CM2CM3CM4CM5CM6CM7CM8CM9CM10CM11CM12CM13CM14CM15CM16CM17CM18CMDental billing The billing schedule for dental X-rays specifies a fixed amount for the office visit plus a fixed amount for each X-ray exposure. If 2 X-rays cost 37 and 4 cost 54, find the cost of 5 exposures.Automobile collisions The energy dissipated in an auto mobile collision varies directly with the square of the speed. By what factor does the energy increase in a 50-mph collision compared with a 20-mph collision?21CM22CM23CM24CM25CM26CM27CM28CM29CM30CM31CM32CM33CM34CM35CM36CM37CM38CM39CM40CMFind the vertex of the graph of the quadratic function f(x)=2(x+5)24.2SC3SC4SCFind the largest area possible if the association has 1200 feet of fencing available.A company that makes and sells baseball caps has found that the total monthly cost C in dollars of producing x caps is given by the function C(x)=0.2x280x+9000. Find the production level that will minimize the monthly cost and find the minimum cost.Fill in the blanks. A quadratic function is defined by the equation ________________ (a0).2E3E4E5E6E7E8EDetermine whether the graph of each quadratic function opens upward or downward. State whether a maximum or minimum point occurs at the vertex of the parabola. f(x)=12x2+310E11E12EDetermine whether the graph of each quadratic function opens upward or downward. State whether a maximum or minimum point occurs at the vertex of the parabola. f(x)=2x2+5x114EFind the vertex of each parabola. f(x)=x2116EFind the vertex of each parabola. f(x)=(x3)2+5Find the vertex of each parabola. f(x)=2(x3)2+4Find the vertex of each parabola. f(x)=2(x+6)2420EFind the vertex of each parabola. f(x)=23(x3)222EFind the vertex of each parabola. f(x)=x24x+424EFind the vertex of each parabola. f(x)=x2+6x326EFind the vertex of each parabola. f(x)=2x2+12x1728EFind the vertex of each parabola. f(x)=3x24x+530EFind the vertex of each parabola. f(x)=12x2+4x332EGraph each quadratic function given in standard form. Identify the vertex, intercepts and axis of symmetry. f(x)=x2434EGraph each quadratic function given in standard form. Identify the vertex, intercepts and axis of symmetry. f(x)=3x2+636EGraph each quadratic function given in standard form. Identify the vertex, intercepts and axis of symmetry. f(x)=12x2+838EGraph each quadratic function given in standard form. Identify the vertex, intercepts and axis of symmetry. f(x)=(x3)2140E41E42E43E44EGraph each quadratic function given in standard form. Identify the vertex, intercepts and axis of symmetry. f(x)=3(x2)2+646EGraph each quadratic function given in standard form. Identify the vertex, intercepts and axis of symmetry. f(x)=13(x1)2348EGraph each quadratic function given in general form. Identify the vertex, intercepts, and axis of symmetry. f(x)=x2+2x50EGraph each quadratic function given in general form. Identify the vertex, intercepts, and axis of symmetry. f(x)=x26x752EGraph each quadratic function given in general form. Identify the vertex, intercepts, and axis of symmetry. f(x)=x24x+154EGraph each quadratic function given in general form. Identify the vertex, intercepts, and axis of symmetry. f(x)=2x212x+1056E57E58E59E60EPolice investigations A police officer seals off the scene of an accident using a roll of yellow tape that is 300 feet long. What dimensions should be used to seal off the maximum rectangular area around the collision? Find the maximum area.62EMaximizing land area Jake has 800 feet of fencing to enclose a rectangular plot of land that borders a river. If Jake doesnt need a fence along the side of the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?Maximizing parking lot area A rectangular parking lot is being constructed for your college football stadium. If the parking lot is bordered on one side by a street and there 750 yards of fencing available for the other three sides, find the length and width of the lot that will maximize the area. What is the largest are that can be enclosed?Maximizing storage are A farmer wants to partition a rectangular feet storage are in a corner of his barn, as shown in the illustration. The barn walls from two sides of the stall, and the farmer has 50 feet of partition for the remaining two sides. What dimensions will maximize the area?Maximizing grazing are A rancher wishes to enclose a rectangular partitioned corral with 1800 feet of fencing. See the illustration. What dimensions of the corral would enclose the largest possible area? Find the maximum area.Sheet metal fabrication A 24-inch-wide sheet of metal is to be bent into a rectangular trough with the cross section shown in the illustration. Find the dimensions that will maximize the amount of water the trough can hold. That is, find the dimensions that will maximize the cross-sectional area.68E69EPath of a guided missile A guided missile is propelled from the origin of a coordinate system with the x-axis along the ground and the y-axis vertical. Its path, or trajectory, is given by the equation y=400x16x2. Find the objects maximum height.Height of a basketball The path of a basketball thrown from the free throw line can be modeled by the quadratic function f(x)=0.06x2+1.5x+6, where x is the horizontal distance in feet from the free throw line and f(x) is the height in feet of the ball. Find the maximum height of the basketball.Projectile motion Devin throws a ball up a hill that makes an angle of 45 with the horizontal. The ball lands 100 feet up the hill. Its trajectory is a parabola with equation y=x2+ax for some number a. Find a.Height of a football A football is thrown by a quarterback from the 10-yard line and caught by the wide receiver on the 50-yard line. The footballs path on this interval can be modeled by the quadratic function f(x)=120x2+3x19, where x is the horizontal distance in yards from the goal line and f(x) is the height of the football in feet. Find the maximum height reached by the football.