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Questions and Answers of College Algebra

Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = x5 - 6x4 + 14x3 - 20x2 + 24x - 16
The table lists the annual amount (in billions of dollars) spent by the federal government on health research and training programs over a 10-yr period.Which one of the following provides the best
Find a rational function f having the graph shown. y 23 -3-2 -6 t.
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = 9x4 + 30x3 + 241x2 + 720x + 600
For any function y = ƒ(x), the following hold true.(a) The real solutions of ƒ(x) = 0 correspond to the x-intercepts of the graph.(b) The real solutions of ƒ(x) < 0 are the x-values for which
For any function y = ƒ(x), the following hold true.(a) The real solutions of ƒ(x) = 0 correspond to the x-intercepts of the graph.(b) The real solutions of ƒ(x) < 0 are the x-values for which
For any function y = ƒ(x), the following hold true.(a) The real solutions of ƒ(x) = 0 correspond to the x-intercepts of the graph.(b) The real solutions of ƒ(x) < 0 are the x-values for which
For any function y = ƒ(x), the following hold true.(a) The real solutions of ƒ(x) = 0 correspond to the x-intercepts of the graph.(b) The real solutions of ƒ(x) < 0 are the x-values for which
For any function y = ƒ(x), the following hold true.(a) The real solutions of ƒ(x) = 0 correspond to the x-intercepts of the graph.(b) The real solutions of ƒ(x) < 0 are the x-values for which
Grandfather clocks use pendulums to keep accurate time. The relationship between the length of a pendulum L and the time T for one complete oscillation can be expressed by the equation L = kTn, where
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = 2x4 - x3 + 7x2 - 4x - 4
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = 32x4 - 188x3 + 261x2 + 54x - 27
Find a rational function f having the graph shown. 3. -3 t. -3
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = 5x3 - 9x2 + 28x + 6
Find a rational function f having the graph shown. y 3- 2 -3 -3-
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = 4x3 + 3x2 + 8x + 6
Find a rational function f having the graph shown. HIP -4-2
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = x4 + 29x2 + 100
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = x4 + 4x3 + 6x2 + 4x + 1
Consider the following “monster” rational function.Analyzing this function will synthesize many of the concepts of this and earlier sections.What are the x-intercepts of the graph of ƒ? x* –
In 1545, a method of solving a cubic equation of the form x3 + mx = n, developed by Niccolo Tartaglia, was published in the Ars Magna, a work by Girolamo Cardano. The formula for finding the one real
Consider the following “monster” rational function.Analyzing this function will synthesize many of the concepts of this and earlier sections.(a) Given that 1 and 2 are zeros of the denominator,
If c and d are complex numbers, prove each statement.c2̅ = (c̅)2
Consider the following “monster” rational function.Analyzing this function will synthesize many of the concepts of this and earlier sections.Given that -4 and -1 are zeros of the numerator,
If c and d are complex numbers, prove each statement.a̅ = a for any real number a
Consider the following “monster” rational function.Analyzing this function will synthesize many of the concepts of this and earlier sections.Find the equation of the horizontal asymptote. x* –
Suppose an economist determines thatwhere y = R(x) is government revenue in tens of millions of dollars for a tax rate of x percent, with y = R(x) valid for 50 … x … 100. Find the revenue for
If c and d are complex numbers, prove each statement. c + d=T +d
Economist Arthur Laffer has been a center of controversy because of his Laffer curve, an idealized version of which is shown here.According to this curve, increasing a tax rate, say from x1 percent
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = x6 - x5 - 26x4 + 44x3 + 91x2 - 139x + 30
The grade x of a hill is a measure of its steepness. For example, if a road rises 10 ft for every 100 ft of horizontal distance, then it has an uphill grade ofGrades are typically kept quite
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = x6 - 9x4 - 16x2 + 144
Braking distance for automobiles traveling at x miles per hour, where 20 ≤ x ≤ 70, can be modeled by the rational function(a) Use graphing to estimate x to the nearest unit when d(x) =
Queuing theory (also known as waiting-line theory) investigates the problem of providing adequate service economically to customers waiting in line. Suppose customers arrive at a fast-food service
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = 12x4 - 43x3 + 50x2 + 38x - 12
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = x4 - 8x3 + 29x2 - 66x + 72
Let the average number of vehicles arriving at the gate of an amusement park per minute be equal to k, and let the average number of vehicles admitted by the park attendants be equal to r. Then the
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = 4x4 - 65x2 + 16
Use a graphing calculator to graph the rational function in each specified exercise. Then use the graph to find ƒ(1.25).Exercise 91 x² – 9 f(x) x + 3
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = x4 - 6x3 + 7x2
Use a graphing calculator to graph the rational function in each specified exercise. Then use the graph to find ƒ(1.25).Exercise 89 x2 + 2х f(x) 2х — 1
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = x4 - 8x3 + 24x2 - 32x + 16
Use a graphing calculator to graph the rational function in each specified exercise. Then use the graph to find ƒ(1.25).Exercise 67 Зx f(x) x2 — х — 2
Use a graphing calculator to graph the rational function in each specified exercise. Then use the graph to find ƒ(1.25).Exercise 61 x + 1 f(x) х — 4
Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.ƒ(x) = x4 + 2x2 + 1
A cylindrical can makes the most efficient use of materials when its height is the same as the diameter of its top. (a) Express the volume V of such a can as a function of the diameter d of its
The formula for the volume of a sphere is V(r) = 4/3 πr3, where r represents the radius of the sphere. Construct a model function V representing the amount of volume gained when the radius r (in
Suppose the length of a rectangle is twice its width. Let x represent the width of the rectangle. Write a formula for the perimeter P of the rectangle in terms of x alone. Then use P(x) notation to
There are 36 in. in 1 yd, and there are 1760 yd in 1 mi. Express the number of inches in x miles by forming two functions and then considering their composition.
The graphs of two functions ƒ and g are shown in the figures.Find (g ° f)(3). y (3, 4) (4, 8) y = f(x) y = g(x) (2, 2) (2, 1) х х 4 (1, –1) об 2.
The graphs of two functions ƒ and g are shown in the figures.Find (ƒ ° g)(2). y (3, 4) (4, 8) y = f(x) y = g(x) (2, 2) (2, 1) х х 4 (1, –1) об 2.
Use the tables for ƒ and g to evaluate each expression.(f ° g)(3) g(x) f(x) 2 -2 4 4 3 -2 4 4 2. 3. 2. 2.
Use the tables for ƒ and g to evaluate each expression.(g ° ƒ)(-2) g(x) f(x) 2 -2 4 4 3 -2 4 4 2. 3. 2. 2.
Use the table to evaluate each expression, if possible. (0) ఉం f(x) g(x) -1 -2 5 3 9. 3.
Use the table to evaluate each expression, if possible.(ƒg)(-1) f(x) g(x) -1 3 -2 3
Use the table to evaluate each expression, if possible.(ƒ - g)(3) f(x) g(x) -1 3 -2 3
Use the table to evaluate each expression, if possible.(ƒ + g)(1) f(x) g(x) -1 3 -2 3
Let ƒ(x) = √x - 2 and g(x) = x2. Find each of the following, if possible.The domain of ƒ ° g
Let ƒ(x) = √x - 2 and g(x) = x2. Find each of the following, if possible.(g ° ƒ)(-1)
Let ƒ(x) = √x - 2 and g(x) = x2. Find each of the following, if possible.(ƒ ° g)(-6)
Let ƒ(x) = √x - 2 and g(x) = x2. Find each of the following, if possible.(g ° ƒ) (3)
Let ƒ(x) = √x - 2 and g(x) = x2. Find each of the following, if possible.(ƒ ° g)(x)
Let ƒ(x) = √x - 2 and g(x) = x2. Find each of the following, if possible.(g ° ƒ)(x)
The area of a square is x2 square inches. Suppose that 3 in. is added to one dimension and 1 in. is subtracted from the other dimension. Express the area A(x) of the resulting rectangle as a product
For each function, find and simplifyƒ(x) = x2 - 5x + 3 f(x+ h) – f(x) h + 0.
In the sale room at a clothing store, every item is on sale for half the original price, plus 1 dollar.(a) Write a function g that finds half of x.(b) Write a function ƒ that adds 1 to x.(c) Write
For each function, find and simplifyƒ(x) = 2x + 9 f(x+ h) – f(x) h + 0.
A software author invests his royalties in two accounts for 1 yr.(a) The first account pays 2% simple interest. If he invests x dollars in this account, write an expression for y1 in terms of x,
Let ƒ(x) = 3x2 - 4 and g(x) = x2 - 3x - 4. Find each of the following.The domain of (f/g) (x)
The cost to hire a caterer for a party depends on the number of guests attending. If 100 people attend, the cost per person will be $20. For each person less than 100, the cost will increase by $5.
Let ƒ(x) = 3x2 - 4 and g(x) = x2 - 3x - 4. Find each of the following.The domain of (ƒg)(x)
When a thermal inversion layer is over a city (as happens in Los Angeles), pollutants cannot rise vertically but are trapped below the layer and must disperse horizontally. Assume that a factory
Let ƒ(x) = 3x2 - 4 and g(x) = x2 - 3x - 4. Find each of the following.(f /g) (-1)
An oil well off the Gulf Coast is leaking, with the leak spreading oil over the water’s surface as a circle. At any time t, in minutes, after the beginning of the leak, the radius of the circular
Let ƒ(x) = 3x2 - 4 and g(x) = x2 - 3x - 4. Find each of the following.(ƒ/g) (3)
The perimeter x of a square with side of length s is given by the formula x = 4s.(a) Solve for s in terms of x.(b) If y represents the area of this square, write y as a function of the perimeter
Let ƒ(x) = 3x2 - 4 and g(x) = x2 - 3x - 4. Find each of the following.(ƒ + g)(2k)
The area of an equilateral triangle with sides of length x is given by the function(a) Find A(2x), the function representing the area of an equilateral triangle with sides of length twice the
Solve each problem.The function ƒ(x) = 3x computes the number of feet in x yards, and the function g(x) = 1760x computes the number of yards in x miles. What is (ƒ ° g)(x), and what does it
Complete the right half of the graph of y = ƒ(x) in the figure for each condition.(a) ƒ is odd.(b) ƒ is even. y = f(x) -2 х 2.
Let ƒ(x) = 3x2 - 4 and g(x) = x2 - 3x - 4. Find each of the following.(ƒ + g)(-4)
Let ƒ(x) = 3x2 - 4 and g(x) = x2 - 3x - 4. Find each of the following.(ƒ - g)(4)
Solve each problem.The function ƒ(x) = 12x computes the number of inches in x feet, and the function g(x) = 5280x computes the number of feet in x miles. What is (ƒ° g)(x), and what does it
Work each problem.Complete the left half of the graph of y = ƒ(x) in the figure for each condition.(a) ƒ(-x) = ƒ(x) (b) ƒ(-x) = -ƒ(x) y 2 y = f(x)
Let ƒ(x) = 3x2 - 4 and g(x) = x2 - 3x - 4. Find each of the following.(ƒg)(x)
Work each problem.Find a function g(x) = ax + b whose graph can be obtained by translating the graph of ƒ(x) = 3 - x down 2 units and 3 units to the right.
Must the domain of g be a subset of the domain of ƒ ° g?
Find functions ƒ and g such that (ƒ ° g)(x) = h(x). (There are many possible ways to do this.) |h(x) = V2x + 3 – 4 ' — 4
Find functions ƒ and g such that (ƒ ° g)(x) = h(x). (There are many possible ways to do this.)h(x) = √6x + 12
Work each problem.Find a function g(x) = ax + b whose graph can be obtained by translating the graph of ƒ(x) = 2x + 5 up 2 units and 3 units to the left.
Each of the following graphs is obtained from the graph of ƒ(x) = |x| or g(x) = √x by applying several of the transformations discussed in this section. Describe the transformations and give an
Decide whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.x2 + (y - 2)2 = 4
A ball is thrown straight up into the air. The function y = h(t) in the graph gives the height of the ball (in feet) at t seconds. The graph does not show the path of the ball. The ball is rising
Decide whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.x2 - y2 = 0
The graph shows the daily megawatts of electricity used on a record-breaking summer day in Sacramento, California.(a) Is this the graph of a function?(b) What is the domain?(c) Estimate the number of
Decide whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.|x| = |y|
Each of the following graphs is obtained from the graph of ƒ(x) = |x| or g(x) = √x by applying several of the transformations discussed in this section. Describe the transformations and give an
Decide whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these.y = 1
Determine the largest open intervals of the domain over which each function is (a) increasing, (b) decreasing, and (c) constant. - х 12 -2 (0, –2) (-1,–3) +(1,–3)
The graph of a function ƒ is shown in the figure. Sketch the graph of each function defined as follows.(a) y = ƒ(x) + 3(b) y = ƒ(x - 2)(c) y = ƒ(x + 3) - 2(d) y = |ƒ(x)| .2. х

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