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study help
mathematics
precalculus
Questions and Answers of
Precalculus
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 =
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 =
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 =
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 =
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 =
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 =
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 =
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
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 =
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 =
In April 2009, Peoples Energy had the following rate schedule for natural gas usage in singlefamily residences:Monthly service charge
In April 2009, Nicor Gas had the following rate schedule for natural gas usage in singlefamily residences:Monthly customer charge $8.40Distribution charge1st
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 =
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
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).
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
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
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
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
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
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
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be
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