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mathematics
precalculus

Questions and Answers of Precalculus

In problem, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and
In problem, sketch the graph of each function. Be sure to label at least three points.f(x) = √x
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be
In problem, find the domain of each function.F(x) = x – 2/x3 + x
An economy car rented in Florida from National Car Rental® on a weekly basis costs $95 per week. Extra days cost $24 per day until the day rate exceeds the weekly rate, in which case the weekly rate
In problem, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and
In problem, sketch the graph of each function. Be sure to label at least three points.f(x) = 1/x
In problem, find the domain of each function.G(x) = x + 4/x3 - 4x
Holders of credit cards issued by banks, department stores, oil companies, and so on, receive bills each month that state minimum amounts that must be paid by a certain due date. The minimum due
In problem, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be
In problem, find the domain of each function.h(x) = √3x - 12
Refer to Problem 55. The card holder may pay any amount between the minimum due and the total owed. The organization issuing the card charges the card holder interest of 1.5% per month for the first
In problem, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and
In problem, graph each function using the techniques of shifting, compressing or stretching, and reflections. Identify any intercepts on the graph. State the domain and, based on the graph, find the
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be
In problem, find the domain of each function.G(x) = √1 - x
The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the
In problem, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and
In problem, graph each function using the techniques of shifting, compressing or stretching, and reflections. Identify any intercepts on the graph. State the domain and, based on the graph, find the
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be
In problem, find the domain of each function.f(x) = 4/√2x - 9
In problem, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and
In problem, graph each function using the techniques of shifting, compressing or stretching, and reflections. Identify any intercepts on the graph. State the domain and, based on the graph, find the
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be
In problem, find the domain of each function.f(x) = x/√2x - 4
In 2009 the U.S. Postal Service charged $1.17 postage for first-class mail retail flats (such as an 8.5'' by 11 envelope) weighing up to 1 ounce, plus $0.17 for each additional ounce up to 13 ounces.
In problem, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and
In problem, graph each function using the techniques of shifting, compressing or stretching, and reflections. Identify any intercepts on the graph. State the domain and, based on the graph, find the
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be
In problem, find the domain of each function.p(x) = √2/x - 1
Exploration Graph y = x2. Then on the same screen graph y = (x - 2) 2, followed by y = (x - 4) 2, followed by y = (x + 2) 2. What pattern do you observe? Can you predict the graph of y = (x
Exploration Graph y = x2. Then on the same screen graph y = x2 + 2, followed by y = x2 + 4, followed by y = x2 - 2. What pattern do you observe? Can you predict the graph of y = x2 - 4? Of y = x2 + 5?
In problem, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and
In problem,(a) Find the slope of the line and(b) Interpret the slope. Ул - (2, 1) „(0,0) -2 -1H 2 X 2.
The coordinate axes divide the xy-plane into four sections called __________ .
Two nonvertical lines have slopes m1 and m2 respectively. The lines are parallel if ________ and the ________ are unequal; the lines are perpendicular if ________.
True or FalseThe radius of the circle is x2 + y2 = 9 is 3.
In problem, find the domain of each function.p(t) = √2t – 4/3t - 21
Exploration Graph y = |x|. Then on the same screen graph y = 2|x|, followed by y = 4|x|, followed by y = ½ |x|. What pattern do you observe? Can you predict the graph of y = ¼ |x|? Of y = 5|x|?
Find the average rate of change of f(x) = -x3 + 1(a) From 0 to 2(b) From 1 to 3(c) From -1 to 1
In problem, graph each function using the techniques of shifting, compressing or stretching, and reflections. Identify any intercepts on the graph. State the domain and, based on the graph, find the
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be
In problem, find the domain of each function.h(z) = √z + 3/z - 2
Exploration Graph y = x2. Then on the same screen graph y = -x2. What pattern do you observe? Now try y = |x| and y = -|x|. What do you conclude?
Find the average rate of change of g(x) = x3 - 2x + 1(a) From -3 to -2(b) From -1 to 1(c) From 1 to 3
In problem, graph each function using the techniques of shifting, compressing or stretching, and reflections. Identify any intercepts on the graph. State the domain and, based on the graph, find the
In problem, the graph of a function f is illustrated. Use the graph of f as the first step toward graphing each of the following functions:(a) F(x) = f(x) + 3(b) G(x) = f(x + 2)(c) P(x) = -f(x)(d)
In problem, for the given functions and g, find the following. For parts (a)–(d), also find the domain.(a) (f + g) (x)(b) (f – g) (x)(c) (f ∙ g)(x)(d) (f/g) (x)(e) (f + g)(3)(f) (f - g) (4)(g)
Exploration Graph y = √x. Then on the same screen graph y = √-x. What pattern do you observe? Now try y = 2x + 1 and y = 2(-x) + 1. What do you conclude?
Find the average rate of change of h(x) = x2 - 2x + 3(a) From -1 to 1(b) From 0 to 2(c) From 2 to 5
In problem, the graph of a function f is illustrated. Use the graph of f as the first step toward graphing each of the following functions:(a) F(x) = f(x) + 3(b) G(x) = f(x + 2)(c) P(x) = -f(x)(d)
In problem, for the given functions and g, find the following. For parts (a)–(d), also find the domain.(a) (f + g) (x)(b) (f – g) (x)(c) (f ∙ g)(x)(d) (f/g) (x)(e) (f + g)(3)(f) (f - g) (4)(g)
Exploration Graph y = x3. Then on the same screen graph y = (x - 1)3 + 2. Could you have predicted the result?
(a) Find the average rate of change from 1 to 3.(b) Find an equation of the secant line containing (1, f (1)) and (3, f(3)).f(x) = 5x - 2
In problem, graph each function using the techniques of shifting, compressing or stretching, and reflections. Identify any intercepts on the graph. State the domain and, based on the graph, find the
In problem, the graph of a function f is illustrated. Use the graph of f as the first step toward graphing each of the following functions:(a) F(x) = f(x) + 3(b) G(x) = f(x + 2)(c) P(x) = -f(x)(d)
In problem, for the given functions and g, find the following. For parts (a)–(d), also find the domain.(a) (f + g) (x)(b) (f – g) (x)(c) (f ∙ g)(x)(d) (f/g) (x)(e) (f + g)(3)(f) (f - g) (4)(g)
In problem, for the given functions and g, find the following. For parts (a)–(d), also find the domain.(a) (f + g) (x)(b) (f – g) (x)(c) (f ∙ g)(x)(d) (f/g) (x)(e) (f + g)(3)(f) (f - g) (4)(g)
Exploration Graph y = x2, y = x4, and y = x6 on the same screen. What do you notice is the same about each graph? What do you notice that is different?
(a) Find the average rate of change from 2 to 5.(b) Find an equation of the secant line containing (2, f(2)) and (5, f(5)).f(x) = -4x + 1
In problem, graph each function using the techniques of shifting, compressing or stretching, and reflections. Identify any intercepts on the graph. State the domain and, based on the graph, find the
In problem, the graph of a function f is illustrated. Use the graph of f as the first step toward graphing each of the following functions:(a) F(x) = f(x) + 3(b) G(x) = f(x + 2)(c) P(x) = -f(x)(d)
In problem, for the given functions and g, find the following. For parts (a)–(d), also find the domain.(a) (f + g) (x)(b) (f – g) (x)(c) (f ∙ g)(x)(d) (f/g) (x)(e) (f + g)(3)(f) (f - g) (4)(g)
In problem, complete the square of each quadratic expression. Then graph each function using the technique of shifting. (If necessary, refer to Appendix A, Section A.3 to review completing the
(a) Find the average rate of change from -2 to 1.(b) Find an equation of the secant line containing (-2, g(-2)) and (1, g(1)).g(x) = x2 - 2
In problem,(a) Find the domain of each function.(b) Locate any intercepts.(c) Graph each function.(d) Based on the graph, find the range.(e) Is f continuous on its domain? Зx if -2 < x < 1 f(x) = (x
In problem, for the given functions and g, find the following. For parts (a)–(d), also find the domain.(a) (f + g) (x)(b) (f – g) (x)(c) (f ∙ g)(x)(d) (f/g) (x)(e) (f + g)(3)(f) (f - g) (4)(g)
In problem, complete the square of each quadratic expression. Then graph each function using the technique of shifting. (If necessary, refer to Appendix A, Section A.3 to review completing the
Consider the equationIs this a function? What is its domain? What is its range?What is its y-intercept, if any? What are its x-intercepts, if any? Is it even, odd, or neither? How would you describe
(a) Find the average rate of change from -1 to 2.(b) Find an equation of the secant line containing (-1, g(-1)) and (2, g(2)).g(x) = x2 + 1
In problem,(a) Find the domain of each function.(b) Locate any intercepts.(c) Graph each function.(d) Based on the graph, find the range.(e) Is f continuous on its domain? f(x) = Jx-1 if -3 < x < 0
In problem, for the given functions and g, find the following. For parts (a)–(d), also find the domain.(a) (f + g) (x)(b) (f – g) (x)(c) (f ∙ g)(x)(d) (f/g) (x)(e) (f + g)(3)(f) (f - g) (4)(g)
In problem, complete the square of each quadratic expression. Then graph each function using the technique of shifting. (If necessary, refer to Appendix A, Section A.3 to review completing the
Define some functions that pass through (0, 0) and (1, 1) and are increasing for x ≥ 0. Begin your list with y = √x, y = x, and y = x2. Can you propose a general result about such functions?
(a) Find the average rate of change from 2 to 4.(b) Find an equation of the secant line containing (2, h(2)) and (4, h(4)).h(x) = x2 - 2x
In problem,(a) Find the domain of each function.(b) Locate any intercepts.(c) Graph each function.(d) Based on the graph, find the range.(e) Is f continuous on its domain? f(x) = X 1 3x if -4 < x < 0
In problem, complete the square of each quadratic expression. Then graph each function using the technique of shifting. (If necessary, refer to Appendix A, Section A.3 to review completing the
(a) Find the average rate of change from 0 to 3.(b) Find an equation of the secant line containing (0, h(0)) and (3, h(3)).h(x) = -2x2 + x
In problem,(a) Find the domain of each function.(b) Locate any intercepts.(c) Graph each function.(d) Based on the graph, find the range.(e) Is f continuous on its domain? f(x) = [x if -2 x 2 2x -
In problem, for the given functions and g, find the following. For parts (a)–(d), also find the domain.(a) (f + g) (x)(b) (f – g) (x)(c) (f ∙ g)(x)(d) (f/g) (x)(e) (f + g)(3)(f) (f - g) (4)(g)
In problem, complete the square of each quadratic expression. Then graph each function using the technique of shifting. (If necessary, refer to Appendix A, Section A.3 to review completing the
(a) Determine whether g is even, odd, or neither.(b) There is a local minimum value of -54 at 3.Determine the local maximum value.g(x) = x3 - 27x
In problem, for the given functions and g, find the following. For parts (a)–(d), also find the domain.(a) (f + g) (x)(b) (f – g) (x)(c) (f ∙ g)(x)(d) (f/g) (x)(e) (f + g)(3)(f) (f - g) (4)(g)
In problem, complete the square of each quadratic expression. Then graph each function using the technique of shifting. (If necessary, refer to Appendix A, Section A.3 to review completing the
f(x) = -x3 + 12x(a) Determine whether f is even, odd, or neither.(b) There is a local maximum value of 16 at 2.Determine the local minimum value.
In problem, complete the square of each quadratic expression. Then graph each function using the technique of shifting. (If necessary, refer to Appendix A, Section A.3 to review completing the
F(x) = -x4 + 8x2 + 8(a) Determine whether F is even, odd, or neither.(b) There is a local maximum value of 24 at x = 2.Determine a second local maximum value.(c) Suppose the area under the graph of F
A page with dimensions of 8 ½ by inches has a border of uniform width x surrounding the printed matter of the page, as shown in the figure.(a) Develop a model that expresses the area A
In problem, complete the square of each quadratic expression. Then graph each function using the technique of shifting. (If necessary, refer to Appendix A, Section A.3 to review completing the
G(x) = -x4 + 32x2 + 144(a) Determine whether G is even, odd, or neither.(b) There is a local maximum value of 400 at x = 4.Determine a second local maximum value.(c) Suppose the area under the graph
A closed box with a square base is required to have a volume of 10 cubic feet.(a) Build a model that expresses the amount A of material used to make such a box as a function of the length x of a side
The equation y = (x - c)2 defines a family of parabolas, one parabola for each value of c. On one set of coordinate axes, graph the members of the family for c = 0, c = 3, and c = -2.
The average cost per hour in dollars, CÌ…, of producing x riding lawn mowers can be modeled by the function(a) Use a graphing utility to graph CÌ… = CÌ…(x).(b) Determine the number of riding
A rectangle has one vertex in quadrant I on the graph of y = 10 – x2, another at the origin, one on the positive x-axis, and one on the positive y-axis.(a) Express the area A of the rectangle as a
Repeat Problem 75 for the family of parabolas y = x2 + c.Data from problem 75The equation y = (x - c)2 defines a family of parabolas, one parabola for each value of c. On one set of coordinate axes,
The concentration C of a medication in the bloodstream t hours after being administered is modeled by the function(a) After how many hours will the concentration be highest?(b) A woman nursing a
Energy conservation experts estimate that homeowners can save 5% to 10% on winter heating bills by programming their thermostats 5 to 10 degrees lower while sleeping. In the given graph, the
A strain of E-coli Beu 397-recA441 is placed into a nutrient broth at 30° Celsius and allowed to grow. The data shown in the table are collected. The population is measured in grams and the time

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