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

Graph each function.ƒ(x) = 2(x - 2)2 - 4
An equation that defines y as a function of x is given. (a) Rewrite each equation using function notation ƒ(x). (b) Find ƒ(3).x - 4y = 8
Use the graph of y = ƒ(x) to find each function value: (a) ƒ(-2), (b) ƒ(0), (c) ƒ(1), and (d) ƒ(4). -6 ++2+3+41 -2
Use a graphing calculator to try to solve -312x + 62 = -4x + 8 - 2x. Explain what happens. What is the solution set?
Graph each function. f (x) = 2x+1– 2
A firm will break even (no profit and no loss) as long as revenue just equals cost. The value of x (the number of items produced and sold) where C(x) = R(x) is the break-even point. Assume that each of the following can be expressed as a linear function. Find(a) The cost function, (b) The
In 2006, in an effort to end the so-called “steroid era,” Major League Baseball introduced a strict drug-testing policy in order to discourage players from using performance-enhancing drugs. The table shows how overall earned run average, or ERA, changed from 2006 through 2014. Find the average
Given functions f and g, find (a) (ƒ ° g)(x) and its domain, and (b) (g ° ƒ)(x) and its domain.ƒ(x) = 8x + 12, g(x) = 3x - 1
Graph each function.ƒ(x) = -3(x - 2)2 + 1
Use the graph of y = ƒ(x) to find each function value: (a) ƒ(-2), (b) ƒ(0), (c) ƒ(1), and (d) ƒ(4). -2-3+4- 12+3. -2-i-0 IN
If three distinct points A, B, and C in a plane are such that the slopes of nonvertical line segments AB, AC, and BC are equal, then A, B, and C are collinear. Otherwise, they are not. Use this fact to determine whether the three points given are collinear.(-1, 4), (-2, -1), (1, 14)
Graph each function. f(x) = -4x + 2 if x 1 3x - 5 if x > 1
The graph provides a good approximation of the number of mobile homes (in thousands) placed in use in the United States from 2003 through 2013.Mobile Homes Placed in Use(a) Use the given ordered pairs to find the average rate of change in the number of mobile homes per year during this period.(b)
Given functions f and g, find (a) (ƒ ° g)(x) and its domain, and (b) (g ° ƒ)(x) and its domain.ƒ(x) = √x, g(x) = x + 3
Graph each function.ƒ(x) = √x + 2
Use the graph of y = ƒ(x) to find each function value: (a) ƒ(-2), (b) ƒ(0), (c) ƒ(1), and (d) ƒ(4). y 2-1-9H1213 -2 4.
If three distinct points A, B, and C in a plane are such that the slopes of nonvertical line segments AB, AC, and BC are equal, then A, B, and C are collinear. Otherwise, they are not. Use this fact to determine whether the three points given are collinear.(0, -7), (-3, 5), (2, -15)
Graph each function. f(x) = [x + 3 -x+4 ifx
In 1991, there were 61.8 births per thousand for adolescent females aged 15–19. By 2013, this number had decreased to 26.6 births per thousand. Find and interpret the average annual rate of change in teen births per year for this period. Round the answer to the nearest tenth.
Given functions f and g, find (a) (ƒ ° g)(x) and its domain, and (b) (g ° ƒ)(x) and its domain.ƒ(x) = √x, g(x) = x - 1
Graph each function.ƒ(x) = √x - 3
An equation that defines y as a function of x is given. (a) Rewrite each equation using function notation ƒ(x). (b) Find ƒ(3).x + 3y = 12
Given functions f and g, find (a) (ƒ ° g)(x) and its domain, and (b) (g ° ƒ)(x) and its domain.ƒ(x) = x3, g(x) = x2 + 3x - 1
Graph each function.ƒ(x) = -√x
If three distinct points A, B, and C in a plane are such that the slopes of nonvertical line segments AB, AC, and BC are equal, then A, B, and C are collinear. Otherwise, they are not. Use this fact to determine whether the three points given are collinear.(0, 9), (-3, -7), (2, 19)
If x represents an integer, then what is the simplest form of the expression [[x]] + x?
A firm will break even (no profit and no loss) as long as revenue just equals cost. The value of x (the number of items produced and sold) where C(x) = R(x) is the break-even point. Assume that each of the following can be expressed as a linear function. Find(a) The cost function, (b) The
Given functions f and g, find (a) (ƒ ° g)(x) and its domain, and (b) (g ° ƒ)(x) and its domain.ƒ(x) = x + 2, g(x) = x4 + x2 - 4
Graph each function.ƒ(x) = √x - 2
An equation that defines y as a function of x is given. (a) Rewrite each equation using function notation ƒ(x). (b) Find ƒ(3).y + 2x2 = 3 - x
In this section we state that two lines, neither of which is vertical, are perpendicular if and only if their slopes have a product of -1. we outline a partial proof of this for the case where the two lines intersect at the origin.By the converse of the Pythagorean theorem, ifthen triangle POQ is a
Decide whether each statement is true or false. If false, tell why.The graph of an even function is symmetric with respect to the y-axis.
A firm will break even (no profit and no loss) as long as revenue just equals cost. The value of x (the number of items produced and sold) where C(x) = R(x) is the break-even point. Assume that each of the following can be expressed as a linear function. Find(a) The cost function, (b) The
Given functions f and g, find (a) (ƒ ° g)(x) and its domain, and (b) (g ° ƒ)(x) and its domain.ƒ(x) = √x - 1, g(x) = 3x
Graph each function.ƒ(x) = 2√x + 1
An equation that defines y as a function of x is given. (a) Rewrite each equation using function notation ƒ(x). (b) Find ƒ(3).y - 3x2 = 2 + x
Determine whether each function is even, odd, or neither.ƒ(x) = -x3 + 2x
Find a point on the graph of the reflection of y = ƒ(x)(a) Across the x-axis (b) Across the y-axis
Find the slope and y-intercept of each line, and graph it.2x + 3y = 16
Graph each equation.3x + 7y = 14
Find the slope and y-intercept of each line, and graph it.4y = -3x
Graph each equation.2x + 5y = 20
Use the table in Exercise 38 to complete the following table.Exercise 38 (f + 8)(x) (f – g)(x) (fg)(x)| ()(x) -2 4 f(x) g(x) -2 -4 -1 5 4 4
Graph each equation.3y = x
Solve each problem. To visualize the situation, use graph paper and a compass to carefully graph each circle.Suppose that receiving stations P, Q, and R are located on a coordinate plane at the points (3, 1), (5, - 4), and (-1, 4), respectively. The epicenter of an earthquake is determined to be
Find the slope and y-intercept of each line, and graph it.x + 2y = -4
Solve each problem. To visualize the situation, use graph paper and a compass to carefully graph each circle.The locations of three receiving stations and the distances to the epicenter of an earthquake are contained in the following three equations: (x - 2)2 + (y - 1)2 = 25, (x + 2)2 + (y - 2)2 =
For each function, find (a) ƒ(x + h),(b) ƒ(x + h) - ƒ(x), and (c) ƒ(x + h) - ƒ(x)/h.ƒ(x) = 2 - x
Graph each equation.x = -5
Work each of the following.Find the coordinates of all points whose distance from (1, 0) is √10 and whose distance from (5, 4) is √10.
Find the slope of the line satisfying the given conditions.Vertical, through (-8, 5)
For each line, (a) find the slope and (b) sketch the graph.y = 3x + 5
For each function, find (a) ƒ(x + h),(b) ƒ(x + h) - ƒ(x), and (c) ƒ(x + h) - ƒ(x)/h.ƒ(x) = -x2
Without graphing, determine 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 = x2 - x + 8
Write an equation (a) in standard form and (b) in slope-intercept form for each line described.Through (-1, 4), parallel to x + 3y = 5
Find the slope of each line, provided that it has a slope.Through (0, -7) and (3, -7)
Solve each problem.The new vehicle market share (in percent) in the United States for trucks is shown in the graph. Let x = 0 represent 2000, x = 8 represent 2008, and so on.Truck Market Share(a) Use the points on the graph to write equations for the graphs in the intervals 30, 84 and 18, 134.(b)
Work each of the following.Phlash Phelps, the morning radio personality on SiriusXM Satellite Radio’s Sixties on Six Decades channel, is an expert on U.S. geography. He loves traveling around the country to strange, out-of-the-way locations. The photo shows Phlash seated in front of a sign in a
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.ƒ (-3)
For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation.y = x2 + 2
For each line, (a) find the slope and (b) sketch the graph.y = 2x - 4
For each function, find (a) ƒ(x + h),(b) ƒ(x + h) - ƒ(x), and (c) ƒ(x + h) - ƒ(x)/h.ƒ(x) = 1 - x2
Without graphing, determine 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 = x + 15
Write an equation (a) in standard form and (b) in slope-intercept form for each line described.Through (3, -2), parallel to 2x - y = 5
Find the slope of each line, provided that it has a slope.Through (5, 6) and 5, -2)
Solve each problem.A water tank has an inlet pipe with a flow rate of 5 gal per minute and an outlet pipe with a flow rate of 3 gal per minute. A pipe can be either closed or completely open. The graph shows the number of gallons of water in the tank after x minutes. Use the concept of slope to
The distance formula, midpoint formula, and center radius form of the equation of a circle are closely related in the following problem.A circle has a diameter with endpoints (-1, 3) and (5, -9). Find the center-radius form of the equation of this circle.To find the center-radius form, we must find
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.g (-2)
For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. y = Vx – 3 х — 3
For each function, find (a) ƒ(x + h),(b) ƒ(x + h) - ƒ(x), and (c) ƒ(x + h) - ƒ(x)/h.ƒ(x) = 1 + 2x2
Write an equation (a) in standard form and (b) in slope-intercept form for each line described.Through (1, 6), perpendicular to 3x + 5y = 1
Find the slope of each line, provided that it has a slope.11x + 2y = 3
Solve each problem.The graph of y = ƒ(x) represents the amount of water in thousands of gallons remaining in a swimming pool after x days.Water in a Swimming Pool(a) Estimate the initial and final amounts of water contained in the pool.(b) When did the amount of water in the pool remain
Solve each problem.The graph shows the gallons of gasoline y in the gas tank of a car after x hours.(a) Estimate how much gasoline was in the gas tank when x = 3.(b) When did the car burn gasoline at the greatest rate?Gasoline Use 20 16 12 1 2 3 4 Time (in hours) Gasoline (in gallons)
The distance formula, midpoint formula, and center radius form of the equation of a circle are closely related in the following problem.A circle has a diameter with endpoints (-1, 3) and (5, -9). Find the center-radius form of the equation of this circle.There are several ways to find the radius of
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.g (10)
Find the slope of each line, provided that it has a slope.9x - 4y = 2
For each line, (a) find the slope and (b) sketch the graph.-4y = 5x
Determine whether each function is even, odd, or neither.ƒ(x) = x5 - 2x3
For each function, find (a) ƒ(x + h),(b) ƒ(x + h) - ƒ(x), and (c) ƒ(x + h) - ƒ(x)/h.ƒ(x) = 1 + 2x2
Write an equation (a) in standard form and (b) in slope-intercept form for each line described.Through (-2, 0), perpendicular to 8x - 3y = 7
The distance formula, midpoint formula, and center radius form of the equation of a circle are closely related in the following problem.A circle has a diameter with endpoints (-1, 3) and (5, -9). Find the center-radius form of the equation of this circle.Another way to find the radius is to repeat
Solve each problem.Lumber that is used to frame walls of houses is frequently sold in multiples of 2 ft. If the length of a board is not exactly a multiple of 2 ft, there is often no charge for the additional length. For example, if a board measures at least 8 ft, but less than 10 ft, then the
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.ƒ (1/3)
Find the slope of each line, provided that it has a slope.x - 2 = 0
For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation.y = |x - 2|
For each line, (a) find the slope and (b) sketch the graph.5x - 2y = 10
Determine whether each function is even, odd, or neither.ƒ(x) = 0.5x4 - 2x2 + 6
For each function, find (a) ƒ(x + h),(b) ƒ(x + h) - ƒ(x), and (c) ƒ(x + h) - ƒ(x)/h.ƒ(x) = x2 + 3x + 1
Write an equation (a) in standard form and (b) in slope-intercept form for each line described.Through (4, 1), parallel to y = -5
The distance formula, midpoint formula, and center radius form of the equation of a circle are closely related in the following problem.A circle has a diameter with endpoints (-1, 3) and (5, -9). Find the center-radius form of the equation of this circle.There is yet another way to find the radius.
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.f (-7/3)
Solve each problem.The snow depth in a particular location varies throughout the winter. In a typical winter, the snow depth in inches might be approximated by the following function.Here, x represents the time in months with x = 0 representing the beginning of October, x = 1 representing the
Find the slope of each line, provided that it has a slope.x - 5y = 0
For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation.y = - |x + 4|
For each line, (a) find the slope and (b) sketch the graph.4x + 3y = 12
Determine whether each function is even, odd, or neither.ƒ(x) = 0.75x2 + |x| + 4
For each function, find (a) ƒ(x + h),(b) ƒ(x + h) - ƒ(x), and (c) ƒ(x + h) - ƒ(x)/h.ƒ(x) = x2 - 4x + 2
Write an equation (a) in standard form and (b) in slope-intercept form for each line described.Through (-2, -2), parallel to y = 3
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.g (1/2)

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