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study help
mathematics
precalculus
Questions and Answers of
Precalculus
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 or stretching, and reflections. Identify any intercepts on the graph. State the domain and, based on the graph, find the
Find the average rate of change of f(x) = -2x2 + 4(a) From 0 to 2(b) From 1 to 3(c) From 1 to 4
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 or stretching, and reflections. Identify any intercepts on the graph. State the domain and, based on the graph, find the
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)
Two cars are approaching an intersection. One is 2 miles south of the intersection and is moving at a constant speed of 30 miles per hour. At the same time, the other car is 3 miles east of the
In problem, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:(a) The domain and range(b) The intercepts, if any(c) Any symmetry with
In problem, write the function whose graph is the graph of y = x3, but is:Shifted to the right 4 units
In problem, graph each function. if x < 2 1 if x > 2 2 - х f(x) =
In problem, sketch the graph of each function. Be sure to label three points on the graph.f(x) = √x
List the number(s) at which f has a local minimum. What are the local minimum values?In problem, use the graph of the function given. (2, 10) 10 (-2, 6) (-5, 0), (5, 0) -10 -5 [(0,0) 10 (-8, -4) -6
In problem, find f + g, f – g, f ∙ g, and f/g for each pair of functions. State the domain of each of these functions.f(x) = 3x; g(x) = 1 + x + x2
Inscribe a right circular cylinder of height h and radius r in a sphere of fixed radius R. See the illustration. Express the volume V of the cylinder as a function of h.V = Ïr2h. Note also
In problem, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:(a) The domain and range(b) The intercepts, if any(c) Any symmetry with
In problem, write the function whose graph is the graph of y = x3, but is:Shifted up 4 units
In problem, determine whether each relation represents a function. For each function, state the domain and range.{(-3, 5), (-1, 3), (3, 7), (4, 12)}
In problem, sketch the graph of each function. Be sure to label three points on the graph.f(x) = 1/x
In problem, the graph of a function is given. Use the graph to find:(a) The intercepts, if any(b) The domain and range(c) The intervals on which it is increasing, decreasing, or constant(d) Whether
In problem, find f + g, f – g, f ∙ g, and f/g for each pair of functions. State the domain of each of these functions.f(x) = x + 1/x – 1; g(x) = 1/x
Inscribe a right circular cylinder of height h and radius r in a cone of fixed radius R and fixed height H. See the illustration. Express the volume V of the cylinder as a function of r. V = Πr2h.
In problem, write the function whose graph is the graph of y = x3, but is:Shifted up 4 units
In problem, determine whether each relation represents a function. For each function, state the domain and range.{(1, 3), (2, 3), (3, 3), (4, 3)}
In problem, sketch the graph of each function. Be sure to label three points on the graph.f(x) = |x|
In problem, find f + g, f – g, f ∙ g, and f/g for each pair of functions. State the domain of each of these functions.f(x) = 1/x – 3; g(x) = 3/x
In problem, the graph of a function is given. Use the graph to find:(a) The intercepts, if any(b) The domain and range(c) The intervals on which it is increasing, decreasing, or constant(d) Whether
MetroMedia Cable is asked to provide service to a customer whose house is located 2 miles from the road along which the cable is buried. The nearest connection box for the cable is located 5 miles
In problem, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:(a) The domain and range(b) The intercepts, if any(c) Any symmetry with
In problem, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:(a) The domain and range(b) The intercepts, if any(c) Any symmetry with
Shifted down 4 unitsIn problem, write the function whose graph is the graph of y = x3, but is:
In problem, determine whether each relation represents a function. For each function, state the domain and range.{(0, -2), (1, 3), (2, 3), (3, 7)}
In problem, sketch the graph of each function. Be sure to label three points on the graph.f(x) = 3√x
In problem, the graph of a function is given. Use the graph to find:(a) The intercepts, if any(b) The domain and range(c) The intervals on which it is increasing, decreasing, or constant(d) Whether
An island is 2 miles from the nearest point P on a straight shoreline. A town is 12 miles down the shore from P. See the illustration.(a) If a person can row a boat at an average speed of 3 miles per
In problem, answer the questions about the given function.f(x) = 2x2 - x - 1(a) Is the point ( -1, 2) on the graph of f?(b) If x = -2, what is f (x)? What point is on the graph of f?(c) If f(x) = -1,
Reflected about the y-axisIn problem, write the function whose graph is the graph of y = x3, but is:
In problem, sketch the graph of each function. Be sure to label three points on the graph.f(x) = 3
In problem, the graph of a function is given. Use the graph to find:(a) The intercepts, if any(b) The domain and range(c) The intervals on which it is increasing, decreasing, or constant(d) Whether
In problem, find the difference quotient of each function that is, findf(x) = 3x2 - 2x + 4 f(x + h) – f(x) h + 0
Water is poured into a container in the shape of a right circular cone with radius 4 feet and height 16 feet. See the figure. Express the volume V of the water in the cone as a function of the height
Iffind:(a) f(-2)(b) f(0)(c) f(2) if x < 0 if x = 0 if x > 0 f(x) = 2x + 1 2 %3D
Reflected about the x-axisIn problem, write the function whose graph is the graph of y = x3, but is:
In problem, answer the questions about the given function.f(x) = -3x2 + 5x(a) Is the point ( -1, 2) on the graph of f?(b) If x = -2, what is f (x)? What point is on the graph of f?(c) If f(x) = -2,
Using the graph of the function shown:(a) Find the domain and the range of f.(b) List the intercepts.(c) Find f(-2).(d) For what value of x does f(x) = -3?(e) Solve f(x) > 0.(f) Graph y = f(x -
In problem, the graph of a function is given. Use the graph to find:(a) The intercepts, if any(b) The domain and range(c) The intervals on which it is increasing, decreasing, or constant(d) Whether
An open box with a square base is to be made from a square piece of cardboard 24 inches on a side by cutting out a square from each corner and turning up the sides. See the figure.(a) Express the
In problem, answer the questions about the given function.f(x) = x + 2/x - 6(a) Is the point (3, 14) on the graph of f?(b) If x = 4, what is f (x)? What point is on the graph of f?(c) If f(x) = 2,
In problem, determine whether each relation represents a function. For each function, state the domain and range.{(-2, 4), (-1, 1), (0, 0), (1, 1)}
Iffind:(a) f(-2)(b) f(-1)(c) f(0) if x < -1 if x = -1 if x > -1 -3x {0 2x2 + 1 f(x) =
In problem, the graph of a function is given. Use the graph to find:(a) The intercepts, if any(b) The domain and range(c) The intervals on which it is increasing, decreasing, or constant(d) Whether
Using the graph of the function g shown:(a) Find the domain and the range of g.(b) Find g(-1).(c) List the intercepts.(d) For what value of x does g(x) = -3?(e) Solve g(x) > 0.(f) Graph y = g(x -
An open box with a square base is required to have a volume of 10 cubic feet.(a) Express the amount A of material used to make such a box as a function of the length x of a side of the square
In problem, answer the questions about the given function.f(x) = x2 + 2/x + 4(a) Is the point (1, 3/5) on the graph of f?(b) If x = 0, what is f(x)? What point is on the graph of f?(c) If f(x) = 1/2,
In problem, determine whether each relation represents a function. For each function, state the domain and range.{(-2, 16), (-1, 4), (0, 3), (1, 4)}
Iffind(a) f(0)(b) f(1)(c) f(2)(d) f(3) if –1 s xs 2 if 2 < x < 3 S2x – 4 x3 – 2 f(x) =
In problem, the graph of a function is given. Use the graph to find:(a) The intercepts, if any(b) The domain and range(c) The intervals on which it is increasing, decreasing, or constant(d) Whether
In problem, answer the questions about the given function.f(x) = 2x2/x4 + 1(a) Is the point (-1, 1) on the graph of f?(b) If x = 2, what is f(x)? What point is on the graph of f?(c) If f(x) = 1, what
In problem, find the function that is finally graphed after each of the following transformations is applied to the graph of y = √x in the order stated.(1) Shift up 2 units(2) Reflect about the
In problem, determine whether the equation defines y as a function of x.y = x2
Iffind(a) f(-1)(b) f(0)(c) f(1)(d) f(3) if -2 s x < 1 if 1 < x< 4 х f(x) = Зх + 2
In problem, the graph of a function is given. Use the graph to find:(a) The intercepts, if any(b) The domain and range(c) The intervals on which it is increasing, decreasing, or constant(d) Whether
In problem, use the graph of the function to find:(a) The domain and the range of.(b) The intervals on which is increasing, decreasing, or constant.(c) The local minimum values and local maximum
In problem, answer the questions about the given function.f(x) = 2x/x – 2(a) Is the point (1/2, 2/3) on the graph of f?(b) If x = 4, what is f(x)? What point is on the graph of f?(c) If f(x) =1,
In problem, find the function that is finally graphed after each of the following transformations is applied to the graph of y = √x in the order stated.(1) Reflect about the x-axis(2) Shift right 3
In problem, determine whether the equation defines y as a function of x.y = x3
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 if x = 0 if x =
In problem, the graph of a function is given. Use the graph to find:(a) The numbers, if any, at which has a local maximum value. What are the local maximum values?(b) The numbers, if any, at which
In problem, determine (algebraically) whether the given function is even, odd, or neither.f(x) = x3 – 4x
In problem, find the function that is finally graphed after each of the following transformations is applied to the graph of y = √x in the order stated.(1) Reflect about the x-axis(2) Shift up 2
In problem, determine whether the equation defines y as a function of x.y = 1/x
According to physicist Peter Brancazio, the key to a successful foul shot in basketball lies in the arc of the shot. Brancazio determined the optimal angle of the arc from the free-throw line to be
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) = 3x 4 if x # 0 if x =
In problem, the graph of a function is given. Use the graph to find:(a) The numbers, if any, at which has a local maximum value. What are the local maximum values?(b) The numbers, if any, at which
In problem, determine (algebraically) whether the given function is even, odd, or neither.g(x) = 4 + x2/1 + x4
In problem, find the function that is finally graphed after each of the following transformations is applied to the graph of y = √x in the order stated.(1) Shift up 2 units(2) Reflect about the
In problem, determine whether the equation defines y as a function of x.y = |x|
The last player in the NBA to use an underhand foul shot (a granny shot) was Hall of Fame forward Rick Barry who retired in 1980. Barry believes that current NBA players could
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 + 3 3x - 2 if x
In problem, the graph of a function is given. Use the graph to find:(a) The numbers, if any, at which has a local maximum value. What are the local maximum values?(b) The numbers, if any, at which
In problem, determine (algebraically) whether the given function is even, odd, or neither.h(x) = 1/x4 + 1/x2 + 1
If (3, 6) is a point on the graph of y = f(x), which of the following points must be on the graph of y = -f(x)?(a) (6, 3)(b) (6, -3)(c) (3, -6)(d) (-3, 6)
In problem, determine whether the equation defines y as a function of x.y2 = 4 - x2
A golf ball is hit with an initial velocity of 130 feet per second at an inclination of 45° to the horizontal. In physics, it is established that the height h of the golf ball is given by the
In problem, the graph of a function is given. Use the graph to find:(a) The numbers, if any, at which has a local maximum value. What are the local maximum values?(b) The numbers, if any, at which
In problem, determine (algebraically) whether the given function is even, odd, or neither.F(x) = √1 – x2
If (3, 6) is a point on the graph of y = f (x), which of the following points must be on the graph of y = f(-x)?(a) (6, 3)(b) (6, -3)(c) (3, -6)(d) (-3, 6)
In problem, determine whether the equation defines y as a function of x.y = ± √1 - 2x
The cross-sectional area of a beam cut from a log with radius 1 foot is given by the functionwhere x represents the length, in feet, of half the base of the beam. See the figure.(a) Find the domain
In problem, determine algebraically whether each function is even, odd, or neither.f(x) = 4x3
In problem, determine (algebraically) whether the given function is even, odd, or neither.G(x) = 1 – x + x3
In problem, determine whether the equation defines y as a function of x.x = y2
If (1, 3) is a point on the graph of y = f(x), which of the following points must be on the graph of y = 2f (x)?(a) (1, 3/2)(b) (2, 3)(c) (1, 6)(d) (1/2, 3)
A Boeing 747 crosses the Atlantic Ocean (3000 miles) with an airspeed of 500 miles per hour. The cost C (in dollars) per passenger is given bywhere x is the ground speed (airspeed - wind).(a) Use 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) = 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
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