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mathematics
precalculus

Questions and Answers of Precalculus

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) = 2x + 5 -3 -5x if -3
In problem, determine algebraically whether each function is even, odd, or neither.f(x) = 2x4 - x2
In problem, determine (algebraically) whether the given function is even, odd, or neither.H(x) = 1 + x + x2
In problem, determine whether the equation defines y as a function of x.x + y2 = 1
If (4, 2) is a point on the graph of y = f(x), which of the following points must be on the graph of y = f(2x)?(a) (4, 1)(b) (8, 2)(c) (2, 2)(d) (4, 4)
If an object weighs m pounds at sea level, then its weight W (in pounds) at a height of h miles above sea level is given approximately by(a) If Amy weighs 120 pounds at sea level, how much will she
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) = 1 + x 2 t if x < 0
In problem, determine algebraically whether each function is even, odd, or neither.g(x) = -3x3 - 5
In problem, determine (algebraically) whether the given function is even, odd, or neither.f(x) = x/1 + x2
Suppose that the x-intercepts of the graph of y = f(x) are -5 and 3.(a) What are the x-intercepts of the graph of y = f(x + 2)?(b) What are the x-intercepts of the graph of y = f(x - 2)?(c) What are
In problem, determine whether the equation defines y as a function of x.y = 2x2 - 3x + 4
The graph of two functions, f and g, is illustrated. Use the graph to answer parts (a)€“(f).(a) (f + g)(2)(b) (f + g)(4)(c) (f - g)(6)(d) (g - f)(6)(e) (f - g)(2)(f) (f/g) (4) Уд fy=g(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) = Vx if x < 0 if x 0
In problem, determine algebraically whether each function is even, odd, or neither.h(x) = 3x3 + 5
In problem, determine (algebraically) whether the given function is even, odd, or neither.g(x) = 1 + x2/x3
In problem, determine whether the equation defines y as a function of x.y = 3x – 1/x + 2
Suppose that the x-intercepts of the graph of y = f(x) are -8 and 1.(a) What are the x-intercepts of the graph of y = f(x + 4)?(b) What are the x-intercepts of the graph of y = f(x - 3)?(c) What are
Describe how you would proceed to find the domain and range of a function if you were given its graph. How would your strategy change if you were given the equation defining the function instead of
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) = xl if 2 = x < 0 if
In problem, determine algebraically whether each function is even, odd, or neither.F(x) = 3√x
In problem, use a graphing utility to graph each function over the indicated interval. Approximate any local maximum values and local minimum values. Determine where the function is increasing and
In problem, determine whether the equation defines y as a function of x.2x2 + 3y2 = 1
Suppose that the function y = f(x) is increasing on the interval ( -1, 5).(a) Over what interval is the graph of y = f(x + 2) increasing?(b) Over what interval is the graph of y = f(x - 5)
How many x-intercepts can the graph of a function have? How many y-intercepts can the graph of a function have?
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) (2 - x lVx if -3 x <
In problem, determine algebraically whether each function is even, odd, or neither.G(x) = √x
In problem, use a graphing utility to graph each function over the indicated interval. Approximate any local maximum values and local minimum values. Determine where the function is increasing and
In problem, determine whether the equation defines y as a function of x.x2 - 4y2 = 1
Suppose that the function y = f(x) is decreasing on the interval (-2, 7).(a) Over what interval is the graph of y = f(x + 2) decreasing?(b) Over what interval is the graph of y = f(x - 5)
Is a graph that consists of a single point the graph of a function? Can you write the equation of such a function?
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) = 2 int(x)
In problem, determine algebraically whether each function is even, odd, or neither.f(x) = x + |x|
In problem, use a graphing utility to graph each function over the indicated interval. Approximate any local maximum values and local minimum values. Determine where the function is increasing and
In problem, find the following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = 3x2 + 2x - 4
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
Match each of the following functions with the graph that best describes the situation.(a) The cost of building a house as a function of its square footage(b) The height of an egg dropped from a
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) = 2 int(2x)
In problem, determine algebraically whether each function is even, odd, or neither.f(x) = 3√2x2 + 1
In problem, use a graphing utility to graph each function over the indicated interval. Approximate any local maximum values and local minimum values. Determine where the function is increasing and
In problem, find the domain of each function.q(x) = √-x - 2
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 following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = -2x2 + x - 1
Match each of the following functions with the graph that best describes the situation.(a) The temperature of a bowl of soup as a function of time(b) The number of hours of daylight per day over a
In problem, the graph of a piecewise-defined function is given. Write a definition for each function. y (2, 1) (-1, 1) . (0, 0) -2
In problem, determine algebraically whether each function is even, odd, or neither.g(x) = 1/x2
In problem, find the average rate of change of f:(a) From 1 to 2(b) From 0 to 1(c) From 2 to 4f(x) = 8x2 – x
In problem, find the following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = x/x2 + 1
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
Consider the following scenario: Barbara decides to take a walk. She leaves home, walks 2 blocks in 5 minutes at a constant speed, and realizes that she forgot to lock the door. So Barbara runs home
In problem, the graph of a piecewise-defined function is given. Write a definition for each function. y 2 (2, 1) |(0, 0) -2 (-1, –1) |
In problem, find the average rate of change of f:(a) From 1 to 2(b) From 0 to 1(c) From 2 to 4f(x) = 2x3 + x
In problem, find the following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = x2 – 1/x + 4
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
Consider the following scenario: Jayne enjoys riding her bicycle through the woods. At the forest preserve, she gets on her bicycle and rides up a 2000-foot incline in 10 minutes. She then travels
In problem, the graph of a piecewise-defined function is given. Write a definition for each function. У 2 (1, 1) (-1, 1) (0, 0) (2, 0) х -2
In problem, determine algebraically whether each function is even, odd, or neither.h(x) = -x3/3x2 - 9
In problem, find the average rate of change from 2 to 3 for each function f. Be sure to simplify.f(x) = 2 - 5x
In problem, find the following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = |x| + 4
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, the graph of a piecewise-defined function is given. Write a definition for each function. y (0, 2), (2, 2) (1, 1) (-1, 0) -2 2 X
In problem, determine algebraically whether each function is even, odd, or neither.F(x) = 2x/|x|
In problem, find the average rate of change from 2 to 3 for each function f. Be sure to simplify.f(x) = 2x2 + 7
In problem, find the following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = √2x2 + 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
The following sketch represents the speed Ï… (in miles per hour) of Michael€™s car as a function of time t (in minutes).(a) Over what interval of time was Michael traveling
If f(x) = int(2x), find(a) f(1.2)(b) f(1.6)(c) f(-1.8)
In problem, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. УА (1, 4) (3, 3) (2, 2) (5, 1) X. 2.
In problem, find the average rate of change from 2 to 3 for each function f. Be sure to simplify.f(x) = 3x - 4x2
In problem, find the following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = 2x + 1/3x - 5
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
If f (x) = int(x/2), find(a) f(1.2)(b) f(1.6)(c) f (-1.8)
In problem, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. УА (4, 4) |(0, 2) (1, 1) (5, 0) 5 2.
In problem, find the average rate of change from 2 to 3 for each function f. Be sure to simplify.f(x) = x2 - 3x + 2
In problem, find the following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = 1 – 1/(x + 2)2
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
Is there a function whose graph is symmetric with respect to the x-axis? Explain.
Sprint PCS offers a monthly cellular phone plan for $39.99. It includes 450 anytime minutes and charges $0.45 per minute for additional minutes.The following function is used to compute the monthly
In problem, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. Уд (3, 4) 4 |(0, 3) (4, 3) (1, 1) 3
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) = -5x + 4
In problem, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. УА (2, 4) (1, 3) (0, 1) 3
In problem, find the domain of each function.f(x) = x2 + 2
In problem, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. У, 4 (2, 3) (-1,1) (0, 0) (3, 2) 1 3 -1
In problem, is the graph shown the graph of a function? Уд
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/x2 + 1
In problem, is the graph shown the graph of a function? Уд
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) = x2/x2 + 1
Two 2009 Tax Rate Schedules are given in the accompanying table. If x equals taxable income and y equals the tax due, construct a function y = f(x) for Schedule X. REVISED 2009 TAX RATE SCHEDULES
In problem, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. Уд (3, 2) 2 - (2, 0) (4, 1) т х -1 1 3 (-2, –2) -2 (-1, -3)
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.g(x) = x/x2 - 16
In problem, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. У (1, 3) 2 (-1, 1) (0, 2) (3, 1) | (2, 0) 3 -1 -2
In problem, sketch the graph of each function. Be sure to label at least three points.f(x) = 3√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.h(x) = 2x/x2 - 4
A trucking company transports goods between Chicago and New York, a distance of 960 miles. The company’s policy is to charge, for each pound, $0.50 per mile for the first 100 miles, $0.40 per mile

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