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mathematics
precalculus

Questions and Answers of Precalculus

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.tan–1(–1) = 3π/4
(a) Show that the functionis an odd function.(b) Find the inverse function of f. f(x) = In(x + x² + 1 Vx? +
Use transformations to sketch the graph of the function.y = x2 – 2x + 2
A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. f(t) is the height of a football t seconds after kickoff.
Make a rough sketch of the graph of the function. Do not use a calculator. Just use the graphs given in Figures 3 and 13 and, if necessary, the transformations of Section 1.3.y =
Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. sin-'x tan'x = -1. cos-x
Three runners compete in a 100-meter race. The graph depicts the distance run as a function of time for each runner. Describe in words what the graph tells you about this race. Who
Use the Law of Exponents to rewrite and simplify the expression. (a) b8(2b)4(b) (6y3)4/2y5
The graph of a function f is given.(a) State the value of f (1).(b) Estimate the value of f( €“ 1).(c) For what values of x is f(x) = 1?(d) Estimate the value of x such
Explain how each graph is obtained from the graph of y = f(x).(a) y = f(x) + 8(b) y = f(x + 8)(c) y = 81(x)(d) y = f(84(e) y = –f(x) – 1(f) y = 8f(1/8 x)
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f(s) = f(t), then s = t.
Use the Law of Exponents to rewrite and simplify the expression. (a) 84/3(b) x(3x2)3
Find the domain of the function.f(x) = cos x / 1 – sin x
Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f is a function, then f (s +
Use the Law of Exponents to rewrite and simplify the expression. (a) 4–3/2–8(b) 1/3√x4
In problem, a linear function is given.(a) Determine the slope and y-intercept of each function.(b) Use the slope and y-intercept to graph the linear function.(c) Determine the average rate of change
The following data represent the weight (in grams) of various candy bars and the corresponding number of calories.(a) Draw a scatter diagram of the data treating weight as the independent
In problem, a linear function is given.(a) Determine the slope and y-intercept of each function.(b) Use the slope and y-intercept to graph the linear function.(c) Determine the average rate of change
The following data represent the weight (in grams) of a box of raisins and the number of raisins in the box.(a) Draw a scatter diagram of the data treating weight as the independent variable.(b) What
In problem, a linear function is given.(a) Determine the slope and y-intercept of each function.(b) Use the slope and y-intercept to graph the linear function.(c) Determine the average rate of change
Professor Grant Alexander wanted to find a linear model that relates the number of hours a student plays video games each week, h, to the cumulative grade-point average,G, of the student. He obtained
In problem, a linear function is given.(a) Determine the slope and y-intercept of each function.(b) Use the slope and y-intercept to graph the linear function.(c) Determine the average rate of change
The marketing manager at Levi-Strauss wishes to find a function that relates the demand D for men’s jeans and p, the price of the jeans.The following data were obtained based on a price history of
In problem, determine whether the given function is linear or nonlinear. If it is linear, determine the slope.x …………………… y = f(x)-2 ………………………. 1/4-1
A marketing firm wishes to find a function that relates the sales S of a product and A, the amount spent on advertising the product. The data are obtained from past experience. Advertising and sales
In problem, determine whether the given function is linear or nonlinear. If it is linear, determine the slope.x …………………… y = f(x)-2 …………………..……. -8-1
A biologist would like to know how the age of the mother affects the incidence rate of Down syndrome.The data to the right represent the age of the mother and the incidence rate of Down syndrome per
In problem, determine whether the given function is linear or nonlinear. If it is linear, determine the slope.x …………………… y = f(x)-2 …………………..……. -4-1
Find the line of best fit for the ordered pairs 1, 5 and 3, 8. What is the correlation coefficient for these data? Why is this result reasonable?
In problem, determine whether the given function is linear or nonlinear. If it is linear, determine the slope.x ……………….…… y = f(x)-2 …………………..……. -26-1
In problem, determine whether the given function is linear or nonlinear. If it is linear, determine the slope.x ……………………… y = f(x)-2 …………………..…….…. -4-1
Explain why it does not make sense to interpret the y-intercept in Problem 17.Data from problem 17The following data represent the weight (in grams) of various candy bars and the corresponding number
In problem, determine whether the given function is linear or nonlinear. If it is linear, determine the slope.x ……………………… y = f(x)-2 …………………..…….…. 8-1
The following data represent the square footage and rents (dollars per month) for apartments in the Del Mar area of San Diego, California.Square Footage, x ………………………. Rent per
Refer to Problem 19. Solve G(h) = 0. Provide an interpretation of this result. Find G(0). Provide an interpretation of this result.Age of Mother, x ……………..…………………………..
In problem, determine whether the given function is linear or nonlinear. If it is linear, determine the slope.x ……………………… y = f(x)-2 …………………..…….…. 0-1
An engineer collects the following data showing the speed s of a Toyota Camry and its average miles per gallon,M.Speed, s …………….............…………. Miles per Gallon,
Suppose that f(x) = 4x - 1 and g(x) = -2x + 5.(a) Solve f(x) = 0.(b) Solve f(x) > 0.(c) Solve f(x) = g(x).(d) Solve f(x) ≤ g(x).(e) Graph y = f(x) and y = g(x) and label the point that
The following data represent the percentage of the U.S. population whose age is x who do not have a high school diploma as of March 2005.Age, a ………………………. Percentage without a High
Suppose that f(x) = 3x + 5 and g(x) = -2x + 15.(a) Solve f(x) = 0.(b) Solve f(x) < 0.(c) Solve f(x) = g(x).(d) Solve f(x) ≥ g(x).(e) Graph y = f(x) and y = g(x) and label the point that
In parts (a) €“ (f), use the following figure.(a) Solve g(x) = 20.(b) Solve g(x) = 60.(c) Solve g(x) = 0.(d) Solve g(x) > 20.(e) Solve g(x) ‰¤ 60. (f) Solve 0 < g(x)
In parts (a) and (b) use the following figure.(a) Solve the equation: f(x) = g(x).(b) Solve the inequality: f(x) > g(x). У 3 fx) у 3D дx) (-4, 6)
In parts (a) and (b), use the following figure.(a) Solve the equation: f (x) = g(x).(b) Solve the inequality: g(x) ‰¤ f (x) < h(x). (y = fx) УА (0, 12) (5, 12) y = h(x) (-6,–5)
The cost C, in dollars, of renting a moving truck for a day is modeled by the function C(x) = 0.25x + 35, where x is the number of miles driven.(a) What is the cost if you drive x = 40 miles?(b) If
In parts (a) and (b), use the following figure.(a) Solve the equation: f (x) = g(x).(b) Solve the inequality: g(x) < f (x) ‰¤ h(x). |(0, 7) (-4, 7) y = h(x) х (0, –8)| (7,–8) y =
Phone Charges The monthly cost C, in dollars, for international calls on a certain cellular phone plan is modeled by the function C(x) = 0.38x + 5, where x is the number of minutes used.(a) What is
In problem,(a) Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any.(b) Determine the
Suppose that the quantity supplied S and quantity demanded D of T-shirts at a concert are given by the following functions:S(p) = -200 + 50pD(p) = 1000 - 25pwhere p is the price of a T-shirt.(a) Find
In problem,(a) Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any.(b) Determine the
Suppose that the quantity supplied S and quantity demanded D of hot dogs at a baseball game are given by the following functions:S(p) = -2000 + 3000pD(p) = 10,000 - 1000pwhere p is the price of a hot
In problem,(a) Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any.(b) Determine the
The function T(x) = 0.15 (x - 8350) + 835 represents the tax bill T of a single person whose adjusted gross income is x dollars for income between $8350 and $33,950, inclusive, in 2009.(a) What is
In problem,(a) Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any.(b) Determine the
In 2002, major league baseball signed a labor agreement with the players. In this agreement, any team whose payroll exceeded $136.5 million in 2006 had to pay a luxury tax of 40% (for second
The point at which a company’s profits equal zero is called the company’s break-even point. For problem, let R represent a company’s revenue, let C represent the company’s costs, and let x
The graph of the function f(x) = ax2 + bx + c has vertex at (0, 2) and passes through the point (1, 8). Find a, b, and c.
The marginal cost of a product can be thought of as the cost of producing one additional unit of output. For example, if the marginal cost of producing the 50th product is $6.20, it cost $6.20 to
On one set of coordinate axes, graph the family of parabolas f(x) = x2 + bx + 1 for b = -4, b = 0, and b = 4. Describe the general characteristics of this family.
True or FalseIf the average rate of change of a linear function is 2/3, then if y increases by 3, x will increase by 2.
If f(x) = 3x2 – Bx + 4 and f(-1) = 12, what is the value of B?
If f(x) = 3x + 8/2x – A and f(0) = 2, what is the value of A?
If f(x) = 2x - B/3x + 4 and f(2) = 1/2, what is the value of B?
In problem,(a) Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any.(b) Determine the
In problem,(a) Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any.(b) Determine the
The point at which a company’s profits equal zero is called the company’s break-even point. For problem, let R represent a company’s revenue, let C represent the company’s costs, and let x
In problem,(a) Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any.(b) Determine the
Suppose that a company has just purchased a new computer for $3000. The company chooses to depreciate the computer using the straight-line method over 3 years.(a) Write a linear model that expresses
In problem,(a) Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any.(b) Determine the
Suppose that a company has just purchased a new machine for its manufacturing facility for $120,000. The company chooses to depreciate the machine using the straight-line method over 10 years.(a)
In problem, determine the quadratic function whose graph is given. УА 2 -1 -3 1 x (0, –1) -2- Vertex: (-1, –2) 2.
The simplest cost function is the linear cost function, C(x) = mx + b, where the y-intercept b represents the fixed costs of operating a business and the slope m represents the cost of each item
In problem, determine the quadratic function whose graph is given. УА (0, 5) 4 Vertex: (2, 1) -1 1 3 4 5 X
Refer to Problem 47. Suppose that the landlord of the building increases the bicycle manufacturer’s rent by $100 per month.(a) Assuming that the manufacturer is open for business 20 days per month,
In problem, determine the quadratic function whose graph is given. Уд Vertex: (-3, 5) 4 2 (0, –4) -8
A truck rental company rents a truck for one day by charging $29 plus $0.07 per mile.(a) Write a linear model that relates the cost C, in dollars, of renting the truck to the number x of miles
In problem, determine the quadratic function whose graph is given. 4 Vertex: (2, 3) 2 5 х -1 1 3 (0, –1)
A phone company offers a domestic long distance package by charging $5 plus $0.05 per minute.(a) Write a linear model that relates the cost C, in dollars, of talking x minutes.(b) What is the cost of
In problem, determine the quadratic function whose graph is given. Уд 8 6- (3, 5). 3 -2 Vertex: (1, –3) 2.
The following data represent the price p and quantity demanded per day q of 24" LCD monitor. Price, p (in dollars) …………………. Quantity Demanded, q150
In problem, determine the quadratic function whose graph is given. Vertex: (-2, 6), 9. 6 2- -3 -1 -2 (-4, –2) 4.
The following data represent the various combinations of soda and hot dogs that Yolanda can buy at a baseball game with $60.Soda, s ……………………….. Hot Dogs, h20
In problem, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.f(x) = 2x2 + 12x
In problem, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.f(x) = -2x2 + 12x
In problem, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.f(x) = 2x2 + 12x – 3
Under what circumstances is a linear function f(x) = mx + b odd? Can a linear function ever be even?
In problem, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.f(x) = 4x2 - 8x + 3
Explain how the graph of f(x) = mx + b can be used to solve mx + b > 0.
In problem, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.f(x) = -x2 + 10x - 4
In problem, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.f(x) = -2x2 + 8x + 3
In problem, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.f(x)= -3x2 + 12x + 1
In problem, determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.f(x) = 4x2 - 4x
The graph of the function f(x) = ax2 + bx + c has vertex at (1,4) and passes through the point (-1, -8). Find a, b, and c.
In problem, for the given functions f and g,(a) Graph f and g on the same Cartesian plane.(b) Solve f(x) = g(x).(c) Use the result of part (b) to label the points of intersection of the graphs of f
In problem, for the given functions f and g,(a) Graph f and g on the same Cartesian plane.(b) Solve f(x) = g(x).(c) Use the result of part (b) to label the points of intersection of the graphs of f
In problem, for the given functions f and g,(a) Graph f and g on the same Cartesian plane.(b) Solve f(x) = g(x).(c) Use the result of part (b) to label the points of intersection of the graphs of f
In problem, for the given functions f and g,(a) Graph f and g on the same Cartesian plane.(b) Solve f(x) = g(x).(c) Use the result of part (b) to label the points of intersection of the graphs of f
In problem, for the given functions f and g,(a) Graph f and g on the same Cartesian plane.(b) Solve f(x) = g(x).(c) Use the result of part (b) to label the points of intersection of the graphs of f
In problem, for the given functions f and g,(a) Graph f and g on the same Cartesian plane.(b) Solve f(x) = g(x).(c) Use the result of part (b) to label the points of intersection of the graphs of f

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