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college algebra
Questions and Answers of
College Algebra
The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines ƒ. y х 3
Graph each function. Give the domain and range.g(x) = [[2x - 1]]
Work each of the following.Find all points satisfying x + y = 0 that are 8 units from (-2, 3).
Decide whether each relation defines y as a function of x. Give the domain and range.y = 2/x - 3
For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. —х — 2 у%3х — 2
Find the slope of the line satisfying the given conditions.Horizontal, through (5, 1)
For each function, find (a) ƒ(x + h),(b) ƒ(x + h) - ƒ(x), and (c) ƒ(x + h) - ƒ(x)/h.ƒ(x) = -2x + 5
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.x2 + y2 = 12
Graph the line satisfying the given conditions.Through (0, 5), m = - 2/3
The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines ƒ.
Solve each problem.Assume that postage rates are $0.49 for the first ounce, plus $0.21 for each additional ounce, and that each letter carries one $0.49 stamp and as many $0.21 stamps as necessary.
Decide whether each relation defines y as a function of x. Give the domain and range.y = -7/x - 5
For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. y = -r + 2
Find the slope of the line satisfying the given conditions.Horizontal, through (3, 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) = -4x + 2
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.y2 - x2 = -6
Graph the line satisfying the given conditions.Through (2, -4), m = 3/4
The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines ƒ. y -2 4 -4-
Solve each problem.The cost of parking a car at an hourly parking lot is $3 for the first half-hour and $2 for each additional half-hour or fraction of a half-hour. Graph the function ƒ that models
Work each of the following.Find the equation of the circle of least radius that contains the points (1, 4) and (-3, 2) within or on its boundary.
Choose the correct answer: For function ƒ, the notation ƒ(3) meansA. the variable ƒ times 3, or 3ƒ.B. the value of the dependent variable when the independent variable is 3.C. the value of the
For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation.y = x2
For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation.2x + 3y = 5
Find the slope of the line satisfying the given conditions.Vertical, through (4, -7)
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/x
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 = -4x3 + x
Find the slope of each line, provided that it has a slope.Through (2, -2) and (3, -4)
The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines ƒ. 300 -100- -1 0 -3 3 -300-
Solve each problem.Sketch a graph that depicts the amount of water in a 100-gal tank. The tank is initially empty and then filled at a rate of 5 gal per minute. Immediately after it is full, a pump
Work each of the following.Find all values of y such that the distance between (3, y) and (-2, 9) is 12.
Work each of the following.Suppose that a circle is tangent to both axes, is in the third quadrant, and has radius √2. Find the center-radius form of its equation.
Give an example of a function from everyday life. Fill in the blanks: depends _____________on , so _______________is a function of ____________.
For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation.3x - 2y = 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) = 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 = x3 - x
The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines ƒ. ---150- 50- 5 10 -10 -50
Find the slope of each line, provided that it has a slope.Through (8, 7) and (1/2, -2)
Solve each problem.Sketch a graph showing the distance a person is from home after x hours if he or she drives on a straight road at 40 mph to a park 20 mi away, remains at the park for 2 hr, and
Work each of the following.Find the shortest distance from the origin to the graph of the circle with equation x2 - 16x + y2 - 14y + 88 = 0.
Let ƒ(x) = -3x + 4 and g(x) = -x2 + 4x + 1. Find each of the following. Simplify if necessary.ƒ (0)
The graph shows dollars (in billions) spent for general science and for space/other technologies in selected years.G (x) represents the dollars spent for general science.S (x) represents the dollars
The graph shows dollars (in billions) spent for general science and for space/other technologies in selected years.G (x) represents the dollars spent for general science.S (x) represents the dollars
The graph shows dollars (in billions) spent for general science and for space/other technologies in selected years.G (x) represents the dollars spent for general science.S (x) represents the dollars
Refer to the graph of Associate’s Degrees Earned. If 2004 ≤ k ≤ 2012, T(k) = r, and F(k) = s, then M(k) = __________.
Use the slopes of the line segments to decide in which period (2004–2008 or 2008–2012) the total number of associate’s degrees earned increased more rapidly.
Estimate M(2012) and F(2012), and use the results to estimate T(2012).
The graph shows the number of associate’s degrees earned (in thousands) in the United States from 2004 through 2012.M(x) gives the number of degrees earned by males.F(x) gives the number earned by
For each relation, (a) Find the domain and range, (b) If the relation defines y as a function ƒ of x, rewrite the relation using function notation and find ƒ(-2).x - 4y = -6
Graph each line. Give the domain and range.x = 3
Decide whether each relation defines a function, and give the domain and range.x.......................... y0.......................... 01......................... -12......................... -2
Use each graph to determine an equation of the circle in (a) center-radius form and (b) general form. (-1, 1) -4, -2) (2, –2) (-1, –5)
Graph each piecewise-defined function. (2x + 1 if x 20 if x
For each graph, decide whether y is a function of x. Give the domain and range of each relation. y 53 х По
Determine whether the three points are the vertices of a right triangle.(-2, -8), (0, -4), (-4, -7)
For the pair of functions defined, find (ƒ + g) (x), (ƒ - g) (x), (ƒg) (x), and (f/g) (x). Give the domain of each.ƒ(x) = √5x - 4, g(x) = -1/x
Find the shortest distance from the origin to the graph of the circle with equation x2 + y2 - 10x - 24y + 144 = 0.
Graph each line. Give the domain and range.3x + 2y = 0
Decide whether each relation defines a function, and give the domain and range.x..................... y0..................... 0-1.................... 1-2.................... 2
Use each graph to determine an equation of the circle in (a) center-radius form and (b) general form. (3, 3) (1, 1) (5, 1) х (3, –1)
Graph each piecewise-defined function. if x
For each graph, decide whether y is a function of x. Give the domain and range of each relation. 3 х 2.
Determine whether the three points are the vertices of a right triangle.(-6, -4), (0, -2), (-10, 8)
Graph each function. -2 8(x)
Write an equation for each line described. Give answers in standard form for and in slope-intercept form (if possible).Vertical, through (-6, 4)
For the pair of functions defined, find (ƒ + g) (x), (ƒ - g) (x), (ƒg) (x), and (f/g) (x). Give the domain of each.ƒ(x) = √4x - 1, g(x) = 1/x
Solve each problem.Find the coordinates of the points of intersection of the line y = 2 and the circle with center at (4, 5) and radius 4.
Decide whether each relation defines a function, and give the domain and range. 10 →15 3- 5 19 -27
Dotty starts up a small business manufacturing bobble-head figures of famous soccer players. Her initial cost is $3300. Each figure costs $4.50 to manufacture.(a) Write a cost function C, where x
In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it.Center ( -√3, -√3 B, radius √3
Graph each piecewise-defined function. ´6 – x if x s 3 if x < 3 if x>3 f(x) =
For each graph, decide whether y is a function of x. Give the domain and range of each relation. х -2.. .2.
For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the midpoint M of line segment PQ. P(-V7,8V3), 0(5V7,-3)
Write an equation for each line described. Give answers in standard form for and in slope-intercept form (if possible).x-intercept (-4, 0), y-intercept (0, 3)
For the pair of functions defined, find (ƒ + g) (x), (ƒ - g) (x), (ƒg) (x), and (f/g) (x). Give the domain of each.ƒ(x) = 4x2 + 2x, g(x) = x2 - 3x + 2
Decide whether or not each equation has a circle as its graph. If it does, give the center and the radius.x2 + y2 - 8y - 9 = 0
Graph each line. Give the domain and range.2x + 5y = 10
Graph each line. Give the domain and range.-4x + 3y = 12
Decide whether each relation defines a function, and give the domain and range. 11 17 3 20
Let ƒ(x) = √x + 1 and g(x) = 2x - 7. Find each of the following.(g ° ƒ)(x) and its domain
In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it.Center (√2, √2 B, radius √2
Graph each piecewise-defined function. Sx - 1 ifx s 3 if x>3 f(x) = (2
For each graph, decide whether y is a function of x. Give the domain and range of each relation. 1 х
For the points P and Q, find (a) The distance d(P, Q) (b) The coordinates of the midpoint M of line segment PQ. P(32, 45), Q(2, -5)
Graph each function.g(x) = 2x2
Write an equation for each line described. Give answers in standard form for and in slope-intercept form (if possible).x-intercept (3, 0), y-intercept (0, -2)
For the pair of functions defined, find (ƒ + g) (x), (ƒ - g) (x), (ƒg) (x), and (f/g) (x). Give the domain of each.ƒ(x) = 2x2 - 3x, g(x) = x2 - x + 3
Decide whether or not each equation has a circle as its graph. If it does, give the center and the radius.x2 + y2 - 2x + 10 = 0
Decide whether each relation defines a function, and give the domain and range.{(2, 5), (3, 7), (3, 9), (5, 11)}
Let ƒ(x) = √x + 1 and g(x) = 2x - 7. Find each of the following.(ƒ ° g)(x) and its domain
In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it.Center (-3, -2), radius 6
For each piecewise-defined function, find (a) ƒ(-5), (b) ƒ(-1), (c) ƒ(0), and (d) ƒ(3). if x
For each graph, decide whether y is a function of x. Give the domain and range of each relation. y 4- х .3.
Write an equation for each of the following, and sketch the graph.The line through (-3, 2) and parallel to the line 2x + 3y = 6
For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the midpoint M of line segment PQ.P(-5, -6), Q(7, -1)
Decide whether each relation defines a function.{(-3, 1), (4, 1), (-2, 7)}
Find the center and radius of each circle.x2 + y2 - 6x - 10y + 30 = 0
Determine the intervals of the domain over which each function is continuous. (1, 2)
The graph of y = ƒ(x) is shown here. Sketch the graph of each of the following. Use ordered pairs to indicate three points on the graph.(a) y = ƒ(x) + 2 (b) y = ƒ(x + 2)(c) y =
In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it.Center (0, -3), radius 7
Decide whether each relation defines a function.{(-12, 5), (-10, 3), (8, 3)}
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