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college algebra
Questions and Answers of
College Algebra
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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).
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
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 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).
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).
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
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).
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
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)
The graph depicts the distance y that a person driving a car on a straight road is from home after x hours. Interpret the graph. At what speeds did the car travel?Distance from Home 70 60 50 40 30 20
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