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All Textbook Solutions for College Algebra (MindTap Course List)

4SC 5SC 6SC 7SC 8SC 9SC 10SC Fill in the blanks. If the graph of a function is symmetric about the ___________, it is called an even function.2E 3E 4E Fill in the blanks. If the values of fx get larger as x increases on an interval, we say that the function is _________ on the open interval.Fill in the blanks. If the values of fx get smaller as x increases on an interval, we say that the function is _________ on the open interval.Fill in the blanks. If the values of fx do not change as x increases on an interval, we say that the function is _________ on the open interval.8E Fill in the blanks. A local ________ occurs where a function changes from decreasing to increasing.10E Determine whether each function even, odd, or neither.12E Determine whether each function even, odd, or neither.Determine whether each function even, odd, or neither.Determine whether each function even, odd, or neither.Determine whether each function even, odd, or neither.Determine algebraically whether each function is even, odd, or neither. fx=x4+x2 Determine algebraically whether each function is even, odd, or neither. fx=x3-2x Determine algebraically whether each function is even, odd, or neither. fx=x3+x2 Determine algebraically whether each function is even, odd, or neither. fx=x6-x2 Determine algebraically whether each function is even, odd, or neither. fx=x5+x3 Determine algebraically whether each function is even, odd, or neither. fx=x3-x2 Determine algebraically whether each function is even, odd, or neither. fx=2x3-3x Determine algebraically whether each function is even, odd, or neither. fx=4x2-5 Determine algebraically whether each function is even, odd, or neither. fx=xx2-1 Determine algebraically whether each function is even, odd, or neither. fx=2xx2-9 Determine algebraically whether each function is even, odd, or neither. fx=1x4 Determine algebraically whether each function is even, odd, or neither. fx=-2x2 Determine algebraically whether each function is even, odd, or neither. fx=x+1 Determine algebraically whether each function is even, odd, or neither. fx=2x-5 Determine algebraically whether each function is even, odd, or neither. fx=xx Determine algebraically whether each function is even, odd, or neither. fx=2x-x State the open intervals where each function is increasing, decreasing, or constant.State the open intervals where each function is increasing, decreasing, or constant.State the open intervals where each function is increasing, decreasing, or constant.State the open intervals where each function is increasing, decreasing, or constant.State the open intervals where each function is increasing, decreasing, or constant.State the open intervals where each function is increasing, decreasing, or constant.Use the graph to identify any local maxima and local minima.Use the graph to identify any local maxima and local minima.Use the graph to identify any local maxima and local minima.Use the graph to identify any local maxima and local minima.Use the graph to identify any local maxima and local minima.Use the graph to identify any local maxima and local minima.Use the graph to identify any local maxima and local minima.Use the graph to identify any local maxima and local minima.Use the graph to identify any local maxima and local minima.Use the graph to identify any local maxima and local minima.Evaluate each piecewise-defined function. fx=2x+2ifx03ifx0 a. f-2 b. f0 Evaluate each piecewise-defined function. fx=x-2ifx1x2ifx1 a. f-1 b. f5 Evaluate each piecewise-defined function. fx=2ifx02-xif0x2x+1ifx2 a. f-1 b. f1 c. f2 Evaluate each piecewise-defined function. fx=2xifx03-xif0x2xifx2 a. f-0.5 b. f0 c. f2 Graph each piecewise-defined function. fx=x+2ifx<02ifx0 Graph each piecewise-defined function. fx=2xifx<0-2xifx0 Graph each piecewise-defined function. fx=xifx02ifx0 Graph each piecewise-defined function. fx=-xifx<012xifx>0 Graph each piecewise-defined function. fx=-4-xifx13ifx1 Graph each piecewise-defined function. fx=-5-xifx1-3ifx1 Graph each piecewise-defined function. fx=-xifx<0x2ifx0 60E 61E 62E 63E 64E 65E 66E 67E 68E 69E Graph each function. y=x+2 71E 72E 73E Riding in a taxi A taxicab company charges 3 for a trip upto 1 mile, and 2 for every extra mile or portion of a mile. Graph the ordered pair m,C, where m represents the miles traveled and C represents the cost. Find the cost to ride 1014 miles.75E iPad repair There is a charge of 30, plus 40 per hour or fraction of an hour, to repair an iPad. Graph the points t,C, where t is the time it takes to do the job and C is the cost. If it takes 4 hours to repair the iPad, how much did it cost?Rounding numbers Measurements are rarely exact; they are often rounded to an appropriate precision. Graph the points x,y, where y is the result of rounding the number x to the nearest ten.78E 79E 80E 81E 82E 83E 84E Describe what happens at the point where the graph of a function changes from increasing to decreasing.86E 87E 88E 89E 90E 91E 92E 93E 94E 95E Determine if the statement is true or false. If the statement is false, then correct it and make it true. All functions have a local maximum value and a local minimum value.97E Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f decreases on the interval -,x1 and increases on the interval x1,, then fx1 is a local maximum value.Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.Determine if the statement is true or false. If the statement is false, then correct it and make it true. --=+4 Self Check Find g-f. Let fx=3x2-5x+1 and gx=2x2+x-3.Self Check Find g/f and its domain. Let fx=3x+1 and gx=2x-3.3SC 4SC 5SC 6SC 7SC 8SC 9SC Self Check Let hx=x2-53.Find functions f and g such that fg=h.Self Check Find the CF10. Ft=3t+15 CFt=59Ft-32 1E 2E 3E 4E 5E 6E 7E 8E 9E Fill in the blanks. To be in the domain of the composite function fg, a number x has to be in the ________ of g, and the output of g must be in the _________ of f.Let fx=2x+1and gx=3x-2. Find each function and its domain. f+g Let fx=2x+1and gx=3x-2. Find each function and its domain. f-g Let fx=2x+1and gx=3x-2. Find each function and its domain. fg Let fx=2x+1and gx=3x-2. Find each function and its domain. f/g Let fx=x2+xand gx=x2-1. Find each function and its domain. f-g Let fx=x2+xand gx=x2-1. Find each function and its domain. f+g Let fx=x2+xand gx=x2-1. Find each function and its domain. f/g Let fx=x2+xand gx=x2-1. Find each function and its domain. fg Let fx=x2-7x+3and gx=x2-5x+6. Find each function and its domain. f+g Let fx=x2-7x+3and gx=x2-5x+6. Find each function and its domain. f-g Let fx=x2-7x+3and gx=x2-5x+6. Find each function and its domain. fg Let fx=x2-7x+3and gx=x2-5x+6. Find each function and its domain. f/g Let fx=x2-7and gx=x. Find each function and its domain. f+g Let fx=x2-7and gx=x. Find each function and its domain. f-g Let fx=x2-7and gx=x. Find each function and its domain. f/g Let fx=x2-7and gx=x. Find each function and its domain. fg Let fx=x2-1and gx=3x-2. Find each value, if possible. f+g2 Let fx=x2-1and gx=3x-2. Find each value, if possible. f+g-3 Let fx=x2-1and gx=3x-2. Find each value, if possible. f-g0 30E Let fx=x2-1and gx=3x-2. Find each value, if possible. fg2 32E Let fx=x2-1and gx=3x-2. Find each value, if possible. f/g23 34E Let fx=2x-5and gx=x3. Find each value. f+g8 36E Let fx=2x-5and gx=x3. Find each value. f-g-27 38E Let fx=2x-5and gx=x3. Find each value. fg-1 40E Let fx=2x-5and gx=x3. Find each value. f/g18 42E Find two functions fand g such that hx can be expressed as the function indicated. Several answers are possible. hx=3x2+2x;f+g 44E 45E 46E Find two functions fand g such that hx can be expressed as the function indicated. Several answers are possible. hx=x3x2+1;f-g 48E Find two functions fand g such that hx can be expressed as the function indicated. Several answers are possible. hx=x2+7x-18;fg 50E Let fx=3xand gx=x+1. Determine the domain of each composite function and then find the composite function. fg 52E 53E 54E Let fx=x2and gx=2x. Determine the domain of each composite function and then find the composite function. gf 56E Let fx=x2and gx=2x. Determine the domain of each composite function and then find the composite function. gg Let fx=x2and gx=2x. Determine the domain of each composite function and then find the composite function. ff 59E 60E 61E 62E Let fx=xand gx=x+1. Determine the domain of each composite function and then find the composite function. fg Let fx=xand gx=x+1. Determine the domain of each composite function and then find the composite function. gf 65E 66E Let fx=x+1and gx=x2-1. Determine the domain of each composite function and then find the composite function. gf 68E Let fx=x+1and gx=x2-1. Determine the domain of each composite function and then find the composite function. gg 70E Let fx=1x-1and gx=1x-2. Determine the domain of each composite function and then find the composite function. fg Let fx=1x-1and gx=1x-2. Determine the domain of each composite function and then find the composite function. gf Let fx=1x-1and gx=1x-2. Determine the domain of each composite function and then find the composite function. ff 74E Let fx=2x-5and gx=5x-2. Find each value. fg2 76E Let fx=2x-5and gx=5x-2. Find each value. gf-3 78E Let fx=2x-5and gx=5x-2. Find each value. ff-12 80E Let fx=3x2-2and gx=4x+4. Find each value. fg-3 82E 83E 84E Let fx=3x2-2and gx=4x+4. Find each value. ff3 86E Let fx=2x and gx=x. Find each value. fg100 88E Let fx=2x and gx=x. Find each value. gf132 90E Let fx=2x and gx=x. Find each value. gg81256 Let fx=2x and gx=x. Find each value. ff-35 Find two functions fand g such that the composition fg=h expresses the given correspondence. Several answers are possible. hx=3x-2 94E Find two functions fand g such that the composition fg=h expresses the given correspondence. Several answers are possible. hx=x2-2 96E Find two functions fand g such that the composition fg=h expresses the given correspondence. Several answers are possible. hx=x-22 98E 99E 100E Find two functions fand g such that the composition fg=h expresses the given correspondence. Several answers are possible. hx=x+2 102E Find two functions fand g such that the composition fg=h expresses the given correspondence. Several answers are possible. hx=x 104E Use the graphs of functions f and g to answer each problem. f+g-4 Use the graphs of functions f and g to answer each problem. f-g1 Use the graphs of functions f and g to answer each problem. fg5 108E Use the graphs of functions f and g to answer each problem. fg3 Use the graphs of functions f and g to answer each problem. gf2 Use the graphs of functions f and g to answer each problem. ff-2 112E 113E 114E 115E 116E DVD camcorder Suppose that the functions Rx=300x and Cx=60,000+40x model a companys monthly revenue and cost for producing and selling DVD camcorder. a. Find R-Cx, the function that models the monthly profit, Px. b. Find the companys profit if 500 camcorders are produced and sold in one month.118E Area of an oil spill Suppose an oil spill from a tanker is spreading in the shape of a circular ripple. If the function dt=3t represents the diameter of the spill in inches at time t minutes, express the area, A, of the oil spill as a function of time. Find the area of the oil spill after 2 hours. Round to one decimal place.120E Perimeter of a square Write a formula for the perimeter P of a square of its area A.Ceramics When the temperature of a pot in a kiln is 1200, an artist turns off the heat and leaves the pot to cool at a controlled rate of 18 per hour. Express the temperature of the pot in degrees Celsius as a function of the time t in hours since the kiln was turned off.123E 124E 125E 126E 127E 128E 129E 130E 131E 132E 133E 134E 135E 136E 137E 138E 139E 140E Determine whether fx=x is one-to-one.Determine whether the graph below represents a one-to-one function.If x0, are fx=x2 and gx=x inverse functions?4SC Find f2. Then find f-111. Explain the significance of the result. fx=x3+3 Find the inverse of f when its domain is restricted to the interval 0,. fx=x2+3 7SC 1E 2E 3E 4E Practice Determine whether each function is one-to-one. fx=5 Practice Determine whether each function is one-to-one. fx=-5 Practice Determine whether each function is one-to-one. fx=3x Practice Determine whether each function is one-to-one. fx=12x Practice Determine whether each function is one-to-one. fx=x2+3 10E Practice Determine whether each function is one-to-one. fx=x3+5 12E Practice Determine whether each function is one-to-one. fx=x3-x 14E Practice Determine whether each function is one-to-one. fx=|x|16E Practice Determine whether each function is one-to-one. x 18E Practice Determine whether each function is one-to-one. fx=x3 20E Practice Determine whether each function is one-to-one. fx=x-22;x2 Practice Determine whether each function is one-to-one. fx=1x Use Horizontal Line Test to determine whether each graph represents a one-to-one function.Use Horizontal Line Test to determine whether each graph represents a one-to-one function.Use Horizontal Line Test to determine whether each graph represents a one-to-one function.26E Use Horizontal Line Test to determine whether each graph represents a one-to-one function.Use Horizontal Line Test to determine whether each graph represents a one-to-one function.Verify that the functions are inverses by showing that fg and gf are the identity function. fx=5x and gx=15x 30E 31E 32E Verify that the functions are inverses by showing that fg and gf are the identity function. fx=x5-1 and gx=x+15 Verify that the functions are inverses by showing that fg and gf are the identity function. fx=x5-2 and gx=x+25 Verify that the functions are inverses by showing that fg and gf are the identity function. fx=x+1x and gx=1x-1

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