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mathematics
precalculus

Precalculus 9th edition Michael Sullivan - Solutions

In problem, match each graph to one of the following functions:A. y = x2 + 2B. y = -x2 + 2C. y = |x| + 2D. y = -|x| + 2E. y = (x - 2) 2F. y = -(x + 2) 2G. y = |x - 2|H. y = -|x + 2|I. y = 2x2J. y = -2x2K. y = 2|x|L. y = -2|x| УА 3 -3 3х
True or FalseA function f has a local maximum at c if there is an open interval I containing c so that for all x in I, f(x) ≤ f(c).
In problem, match each graph to one of the following functions:A. y = x2 + 2B. y = -x2 + 2C. y = |x| + 2D. y = -|x| + 2E. y = (x - 2) 2F. y = -(x + 2) 2G. y = |x - 2|H. y = -|x + 2|I. y = 2x2J. y = -2x2K. y = 2|x|L. y = -2|x| -3,
In problem, match each graph to one of the following functions:A. y = x2 + 2B. y = -x2 + 2C. y = |x| + 2D. y = -|x| + 2E. y = (x - 2) 2F. y = -(x + 2) 2G. y = |x - 2|H. y = -|x + 2|I. y = 2x2J. y = -2x2K. y = 2|x|L. y = -2|x| YA 3 -3
Is f decreasing on the interval (-8, -4)?In problem, use the graph of the function given. (2, 10) 10 (-2, 6) (5, 0) (-5, 0) [(0, 0) - 10 -5 10 X 5 (-8, –4) –6-
In problem, match each graph to one of the following functions:A. y = x2 + 2B. y = -x2 + 2C. y = |x| + 2D. y = -|x| + 2E. y = (x - 2) 2F. y = -(x + 2) 2G. y = |x - 2|H. y = -|x + 2|I. y = 2x2J. y = -2x2K. y = 2|x|L. y = -2|x| Ул 5 -3 3х -1F
In problem, match each graph to one of the following functions:A. y = x2 + 2B. y = -x2 + 2C. y = |x| + 2D. y = -|x| + 2E. y = (x - 2) 2F. y = -(x + 2) 2G. y = |x - 2|H. y = -|x + 2|I. y = 2x2J. y = -2x2K. y = 2|x|L. y = -2|x| y. 3х -3
Is f decreasing on the interval (2, 5)?In problem, use the graph of the function given. (2, 10) 10 (-2, 6) (-5, 0), (5, 0) -10 -5 [(0,0) 10 (-8, -4) -6
In problem, match each graph to one of the following functions:A. y = x2 + 2B. y = -x2 + 2C. y = |x| + 2D. y = -|x| + 2E. y = (x - 2) 2F. y = -(x + 2) 2G. y = |x - 2|H. y = -|x + 2|I. y = 2x2J. y = -2x2K. y = 2|x|L. y = -2|x| У. 8 6 x -6
In problem, match each graph to one of the following functions:A. y = x2 + 2B. y = -x2 + 2C. y = |x| + 2D. y = -|x| + 2E. y = (x - 2) 2F. y = -(x + 2) 2G. y = |x - 2|H. y = -|x + 2|I. y = 2x2J. y = -2x2K. y = 2|x|L. y = -2|x| 4 -4 -4
In problem, determine whether each relation represents a function. For each function, state the domain and range. Birthday Person Jan. 8 Elvis Colleen Kaleigh Mar. 15 Sept. 17 Marissa
In problem, match each graph to one of the following functions:A. y = x2 + 2B. y = -x2 + 2C. y = |x| + 2D. y = -|x| + 2E. y = (x - 2) 2F. y = -(x + 2) 2G. y = |x - 2|H. y = -|x + 2|I. y = 2x2J. y = -2x2K. y = 2|x|L. y = -2|x| 3 x -3
An equilateral triangle is inscribed in a circle of radius r. See the figure in Problem 16. Express the area A within the circle, but outside the triangle, as a function of the length x of a side of the triangle.Data from problem 16 First show that ?
In problem, match each graph to one of the following functions:A. y = x2 + 2B. y = -x2 + 2C. y = |x| + 2D. y = -|x| + 2E. y = (x - 2) 2F. y = -(x + 2) 2G. y = |x - 2|H. y = -|x + 2|I. y = 2x2J. y = -2x2K. y = 2|x|L. y = -2|x| УА 4 х -4 -4
In problem, match each graph to one of the following functions:A. y = x2 + 2B. y = -x2 + 2C. y = |x| + 2D. y = -|x| + 2E. y = (x - 2) 2F. y = -(x + 2) 2G. y = |x - 2|H. y = -|x + 2|I. y = 2x2J. y = -2x2K. y = 2|x|L. y = -2|x| УА 3 -3 -3F
In April 2009, Peoples Energy had the following rate schedule for natural gas usage in singlefamily residences:Monthly service charge $15.95Per therm service charge1st 50 therms
In April 2009, Nicor Gas had the following rate schedule for natural gas usage in singlefamily residences:Monthly customer charge $8.40Distribution charge1st 20 therms $0.1473/thermNext 30 therms
Refer to the revised 2009 tax rate schedules. If x equals taxable income and y equals the tax due, construct a function y = f(x) for Schedule Y-1.Revised 2009 tax rate schedules REVISED 2009 TAX RATE SCHEDULES Schedule Y-1-Married Filing jointly or qualifying Widow(er) Schedule X-Single The Tax
Redo problem 57(a) €“ (d) for an air temperature of -10°C.Data from problem 57The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the
Exploration Graph y = x3, y = x5, and y = x7 on the same screen. What do you notice is the same about each graph? What do you notice that is different?
The short-term (no more than 24 hours) parking fee F (in dollars) for parking x hours at O€™Hare International Airport€™s main parking garage can be modeled by the functionDetermine the fee for parking in the short-term parking garage for(a) 2 hours(b) 7 hours(c) 15 hours(d) 8 hours and 24
In problem, sketch the graph of each function. Be sure to label three points on the graph.f(x) = x
In problem, match each graph to its function.A. Constant functionB. Identity functionC. Square functionD. Cube functionE. Square root functionF. Reciprocal functionG. Absolute value functionH. Cube root function
In problem, match each graph to its function.A. Constant functionB. Identity functionC. Square functionD. Cube functionE. Square root functionF. Reciprocal functionG. Absolute value functionH. Cube root function
In problem, match each graph to its function.A. Constant functionB. Identity functionC. Square functionD. Cube functionE. Square root functionF. Reciprocal functionG. Absolute value functionH. Cube root function
In problem, match each graph to its function.A. Constant functionB. Identity functionC. Square functionD. Cube functionE. Square root functionF. Reciprocal functionG. Absolute value functionH. Cube root function
In problem, match each graph to its function.A. Constant functionB. Identity functionC. Square functionD. Cube functionE. Square root functionF. Reciprocal functionG. Absolute value functionH. Cube root function
In problem, match each graph to its function.A. Constant functionB. Identity functionC. Square functionD. Cube functionE. Square root functionF. Reciprocal functionG. Absolute value functionH. Cube root function
The function f(x) = x2 is decreasing on the interval ________.
For the function f(x) = x2, compute each average rate of change:(a) From 0 to 1(b) From 0 to 0.5(c) From 0 to 0.1(d) From 0 to 0.01(e) From 0 to 0.001(f) Use a graphing utility to graph each of the secant lines along with .(g) What do you think is happening to the secant lines?(h) What is happening
In problem, determine which of the given points are on the graph of the equation.Equation: y = x4 – √xPoints: (0, 0); (1, 1); (-1, 0)
In problem, list the intercepts and test for symmetry with respect to the x-axis, the y-axis, and the origin.x2 + 4y2 = 16
True or FalseThe point (-1, 4) lies in quadrant IV of the Cartesian plane.
In problem,(a) Find the slope of the line and(b) Interpret the slope. y. (-2, 1) 2- ,0) -2 2 х -1
In problem, determine which of the given points are on the graph of the equation.Equation: y = x3 – 2√xPoints: (0, 0); (1, 1); (1, -1)
In problem, write the standard form of the equation and the general form of the equation of each circle of radius r and center (h, k). Graph each circle.r = 3; (h, k) = (0, 0)
In problem, list the intercepts and test for symmetry with respect to the x-axis, the y-axis, and the origin.9x2 - y2 = 9
True or FalseThe midpoint of a line segment is found by averaging the x coordinates and averaging the y-coordinates of the endpoints.
In problem,(a) Find the slope of the line and(b) Interpret the slope. yA 2 (1, 1) (-2, 2) 2 X -2 -1
In problem, determine which of the given points are on the graph of the equation.Equation: y2 = x2 + 9Points: (0, 3); (3, 0); (-3, 0)
In problem, list the intercepts and test for symmetry with respect to the x-axis, the y-axis, and the origin.y = x4 + 2x2 + 1
In problem, plot each point in the xy-plane.Tell in which quadrant or on what coordinate axis each point lies.(a) A = (-3, 2)(b) B = (6, 0)(c) C = (-2, -2)(d) E = (6, 5)(e) D = (0, -3)(f) F = (6, -3)
In problem,(a) Find the slope of the line and(b) Interpret the slope. y. (2, 2) (-1, 1) -2 -1
In problem, list the intercepts and test for symmetry with respect to the x-axis, the y-axis, and the origin.y = x3 - x
In problem, plot each point in the xy-plane.Tell in which quadrant or on what coordinate axis each point lies.(a) A = (1, 4)(b) B = (-3, -4)(c) C = (-3, 4)(d) D = (4, 1)(e) E = (0, 1)(f) F = (-3, 0)
In problem, determine which of the given points are on the graph of the equation.Equation: x2 + y2 = 4Points: (0, 2); (-2, 2); (√2, √2)
In problem, list the intercepts and test for symmetry with respect to the x-axis, the y-axis, and the origin.x2 + x + y2 + 2y = 0
Plot the points (2,0), (2, -3), (2, 4), (2, 1) and (2, -1). Describe the set of all points of the form (2, y) where y is a real number.
A wire 10 meters long is to be cut into two pieces. One piece will be shaped as a square, and the other piece will be shaped as a circle. See the figure.(a) Express the total area A enclosed by the pieces of wire as a function of the length x of a side of the square.(b) What is the domain of
True or FalseThe domain of (f ∙ g) (x) consists of the numbers x that are in the domains of both and g.
In problem, graph each equation.3x - 2y = 12
A community skating rink is in the shape of a rectangle with semicircles attached at the ends.The length of the rectangle is 20 feet less than twice the width.The thickness of the ice is 0.75 inch.(a) Build a model that expresses the ice volume, V, as a function of the width, x.(b) How much ice is
In problem, find the domain of each function.f(x) = √x + 2
Is f decreasing on the interval (-8, -4)?In problem, use the graph of the function given. (2, 10) 10 (-2, 6) (5, 0) (-5, 0) [(0, 0) - 10 -5 10 X 5 (-8, –4) –6-
A wire 10 meters long is to be cut into two pieces. One piece will be shaped as an equilateral triangle, and the other piece will be shaped as a circle.(a) Express the total area A enclosed by the pieces of wire as a function of the length x of a side of the equilateral triangle.(b) What is the
In problem, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:(a) The domain and range(b) The intercepts, if any(c) Any symmetry with respect to the x-axis, the y-axis, or the origin УА 3 3х -3 -3
True or FalseThe independent variable is sometimes referred to as the argument of the function.
In problem, graph each equation.x = y2
In problem, find the domain of each function.h(x) = √x/|x|
Is f increasing on the interval (2, 10)?In problem, use the graph of the function given. (2, 10) 10 (-2, 6) (-5, 0) (5, 0) -10 -5 [(0,0) 10 (-8,-4) -6 5
In problem, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:(a) The domain and range(b) The intercepts, if any(c) Any symmetry with respect to the x-axis, the y-axis, or the origin -7 -1
True or FalseIf no domain is specified for a function f, then the domain of is taken to be the set of real numbers.
In problem, graph each equation.x2 + (y - 3) 2 = 16
In problem, find the domain of each function.g(x) = |x|/x
A wire of length x is bent into the shape of a square.(a) Express the perimeter p of the square as a function of x.(b) Express the area A of the square as a function of x.
In problem, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:(a) The domain and range(b) The intercepts, if any(c) Any symmetry with respect to the x-axis, the y-axis, or the origin TT 2
In problem, graph each equation.y = √x
True or False The domain of the function f(x) = x2 - 4/x is {x|x ≠ ± 2}.
In problem, match each graph to its function.A. Constant functionB. Identity functionC. Square functionD. Cube functionE. Square root functionF. Reciprocal functionG. Absolute value functionH. Cube root function
In problem, find the domain of each function.g(x) = x/x2 + 2x - 3
List the interval(s) on which f is increasing.In problem, use the graph of the function given. (2, 10) 10 (-2, 6) (-5, 0) (5, 0) -10 -5 [(0,0) 10 (-8,-4) -6 5
A semicircle of radius r is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle. See the figure.(a) Express the area A of the rectangle as a function of the radius r of the semicircle.(b) Express the perimeter p of the rectangle as a function of r.
For the equation 3x2 - 4y = 12, find the intercepts and check for symmetry.
In problem, find the domain of each function.F(x) = 1/x2 - 3x - 4
List the interval(s) on which f is decreasing.In problem, use the graph of the function given. (2, 10) 10 (-2, 6) (-5, 0) (5, 0) -10 -5 [(0,0) 10 (-8,-4) -6 5
An equilateral triangle is inscribed in a circle of radius r. See the figure. Express the circumference C of the circle as a function of the length x of a side of the triangle.First show that r2 = x2/3. х
Find the slope–intercept form of the equation of the line containing the points (-2, 4) and (6, 8).
Is there a local maximum value at 2? If yes, what is it?In problem, use the graph of the function given. (2, 10) 10 (-2, 6) (-5, 0) (5, 0) -10 -5 [(0,0) 10 (-8,-4) -6 5
In problem, find f + g, f – g, f ∙ g, and f/g for each pair of functions. State the domain of each of these functions.f(x) = 2 - x; g(x) = 3x + 1
In problem, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:(a) The domain and range(b) The intercepts, if any(c) Any symmetry with respect to the x-axis, the y-axis, or the origin y. 3 -3 -3
In problem, graph each function.f(x) = (x + 2)2 - 3
In problem, sketch the graph of each function. Be sure to label three points on the graph.f(x) = x2
Is there a local maximum value at 5? If yes, what is it?In problem, use the graph of the function given. (2, 10) 10 (-2, 6) (-5, 0) (5, 0) -10 -5 [(0,0) 10 (-8,-4) -6 5
In problem, find f + g, f – g, f ∙ g, and f/g for each pair of functions. State the domain of each of these functions.f(x) = 2x - 1; g(x) = 2x + 1
In problem, find the domain of each function.f(x) = √2 - x
Two cars leave an intersection at the same time. One is headed south at a constant speed of 30 miles per hour, and the other is headed west at a constant speed of 40 miles per hour (see the figure). Build a model that expresses the distance d between the cars as a function of the time t.At t = 0,
In problem, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:(a) The domain and range(b) The intercepts, if any(c) Any symmetry with respect to the x-axis, the y-axis, or the origin У (4, 3) -4
In problem, determine whether each relation represents a function. For each function, state the domain and range. Average Income Level of Education Less than 9th grade $18,120 $23,251 $36,055 9th-12th grade High School Graduate Some College College Graduate $45,810 $67,165
In problem, graph each function.f(x) = 1/x
In problem, sketch the graph of each function. Be sure to label three points on the graph.f(x) = x3
List the number(s) at which has a local maximum.What are the local maximum values?In problem, use the graph of the function given. (2, 10) 10 (-2, 6) (-5, 0) (5, 0) -10 -5 [(0,0) 10 (-8,-4) -6 5
In problem, find f + g, f – g, f ∙ g, and f/g for each pair of functions. State the domain of each of these functions.f(x) = 3x2 + x + 1; g(x) = 3x
In problem, find the difference quotient of each function that is, findf(x) = -2x2 + x + 1 f(x + h) – f(x) h + 0
In problem, use the graph of the function to find:(a) The domain and the range of .(b) The intervals on which is increasing, decreasing, or constant.(c) The local minimum values and local maximum values.(d) The absolute maximum and absolute minimum.(e) Whether the graph is symmetric with respect to
In problem, determine algebraically whether each function is even, odd, or neither.h(x) = x/x2 -1
The following sketch represents the distance d (in miles) that Kevin was from home as a function of time t (in hours). Answer the questions based on the graph. In parts (a)€“(g), how many hours elapsed and how far was Kevin from home during this time?(a) From t = 0 to t = 2(b) From t = 2
Draw the graph of a function whose domain is {x|-3 ≤ x ≤ 8, x ≠ 5} and whose range is {y|-1 ≤ y ≤ 2, y ≠ 0}. What point(s) in the rectangle -3 ≤ x ≤ 8, -1 ≤ y ≤ 2 cannot be on the graph? Compare your graph with those of other students What differences do you see?
In problem, is the graph shown the graph of a function? УА
In problem, is the graph shown the graph of a function? УА
In problem, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. Уд (2, 4) 4 - (-1, 3) (0,2) X. -1

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