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College Algebra 12th edition Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels - Solutions

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 the graph lies below the x-axis.(c) The real solutions of ƒ(x) > 0 are the x-values for which the
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 the graph lies below the x-axis.(c) The real solutions of ƒ(x) > 0 are the x-values for which the
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 the graph lies below the x-axis.(c) The real solutions of ƒ(x) > 0 are the x-values for which the
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 the graph lies below the x-axis.(c) The real solutions of ƒ(x) > 0 are the x-values for which the
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 the graph lies below the x-axis.(c) The real solutions of ƒ(x) > 0 are the x-values for which the
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 k is a constant and n is a positive integer to be determined. The data in the table were taken for
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* – 3x3 – 21x² + 43x + 60 f(x) = x4 – 6x3 + x² + 24x – 20
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 solution of the equation isx3 + 9x = 26 2 2 3 n n -n m + ()*+G) -+ G* +G) 3 3 x = 2 3 2 3 m 3
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, factor the denominator completely.(b) Write the entire quotient for ƒ so that the numerator and the
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, factor the numeratorcompletely. x* – 3x3 – 21x² + 43x + 60 f(x) = x4 – 6x3 + x² + 24x – 20
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* – 3x3 – 21x² + 43x + 60 f(x) = x4 – 6x3 + x² + 24x – 20
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 each tax rate. Round to the nearest tenth if necessary.(a) 50% (b) 60% (c) 80% (d) 100%
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 to x2 percent on the graph, can actually lead to a decrease in government revenue. All economists
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 small—usually less than 10%. The braking distance D for a car traveling at 50 mph on a wet, uphill grade
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) = 300.(b) Complete the table for each value of x.(c) If a car doubles its speed, does the braking distance
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 window at the rate of 9 people per hour. With reasonable assumptions, the average time (in hours) that
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 average waiting time T (in minutes) for each vehicle arriving at the park is given by the rational
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 top.(b) Express the surface area S of such a can as a function of the diameter d of its top. d
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 inches) of a sphere is increased by 3 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 describe it as a function. What type of function is this?
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 of two functions.
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 and simplify the function (ƒ ° g)(x).(d) Use the function from part (c) to find the sale price of a
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, where y1 represents the amount of interest earned.(b) He invests in a second account $500 more than
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. Assume that no more than 100 people will attend. Let x represent the number less than 100 who do not
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 smokestack begins emitting a pollutant at 8 a.m. Assume that the pollutant disperses horizontally over a
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 oil slick on the surface is r(t) = 4t feet. Let A(r) = πr2 represent the area of a circle of radius
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 x.(c) Use the composite function of part (b) to find the area of a square with perimeter 6.
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 original length.(b) Find the area of an equilateral triangle with side length 16. Use the formula A(2x)
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 compute?
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 compute?
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 equation for the graph. y х -2 -4 2.
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 straight up and then falling straight down.(a) What is the height of the ball at 2 sec?(b) When will
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 megawatts used at 8 a.m.(d) At what time was the most electricity used? the least electricity?(e)
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 equation for the graph. y х -3 ПГННН
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
Find functions ƒ and g such that (ƒ ° g)(x) = h(x). (There are many possible ways to do this.)h(x) = (2x - 3)3
Suppose that for a function f, ƒ(3) = 6. For the given assumptions, find another function value.ƒ is an odd function.

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