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study help
mathematics
precalculus
Questions and Answers of
Precalculus
Problem requires the following discussion of a secant line. The slope of the secant line containing the two points (x, f (x)) and (x + h, f (x + h)) on the graph of a function y = f (x) may be given
The graph of a function f is illustrated in the figure.(a) Draw the graph of y = |f(x)|.(b) Draw the graph of y = f (|x|). Уд (1, 1) -3 (2, 0) 3 x (-2, –1) (-1, –1) -2- 2.
Problem requires the following discussion of a secant line. The slope of the secant line containing the two points (x, f (x)) and (x + h, f (x + h)) on the graph of a function y = f (x) may be given
The graph of a function f is illustrated in the figure.(a) Draw the graph of y = |f(x)|.(b) Draw the graph of y = f (|x|). УА 2 (1, 1) (-2, 0) (2, 0) -3 3х (-1, –1) -2
Problem requires the following discussion of a secant line. The slope of the secant line containing the two points (x, f (x)) and (x + h, f (x + h)) on the graph of a function y = f (x) may be given
Suppose (1, 3) is a point on the graph of y = f (x).(a) What point is on the graph of y = f (x + 3) -5?(b) What point is on the graph of y = -2f (x - 2) +1?(c) What point is on the graph of y = f (2x
Problem requires the following discussion of a secant line. The slope of the secant line containing the two points (x, f (x)) and (x + h, f (x + h)) on the graph of a function y = f (x) may be given
Suppose (-3, 5) is a point on the graph of y = g(x).(a) What point is on the graph of y = g(x + 1) -3?(b) What point is on the graph of y = -3g(x - 4) + 3?(c) What point is on the graph of y = g(3x +
Problem requires the following discussion of a secant line. The slope of the secant line containing the two points (x, f (x)) and (x + h, f (x + h)) on the graph of a function y = f (x) may be given
Suppose that the graph of a function f is known. Explain how the graph of y = 4f(x) differs from the graph of y = f(4x).
Problem requires the following discussion of a secant line. The slope of the secant line containing the two points (x, f (x)) and (x + h, f (x + h)) on the graph of a function y = f (x) may be given
If f(x) = 2x - A/x - 3 and f(4) = 0, what is the value of A? Where is not defined?
Suppose that the graph of a function f is known. Explain how the graph of y = f(x) - 2 differs from the graph of y = f(x - 2).
Problem requires the following discussion of a secant line. The slope of the secant line containing the two points (x, f (x)) and (x + h, f (x + h)) on the graph of a function y = f(x) may be given
If f(x) = x - B/x – A, f(2) = 0 and f(1) what is the values of A and B?
The area under the curve y = √x bounded below by the x-axis and on the right by x = 4 is 16/3 square units. Using the ideas presented in this section, what do you think is the area under the curve
Problem requires the following discussion of a secant line. The slope of the secant line containing the two points (x, f (x)) and (x + h, f (x + h)) on the graph of a function y = f (x) may be given
Express the area A of a rectangle as a function of the length x if the length of the rectangle is twice its width.
Draw the graph of a function that has the following properties: domain: all real numbers; range: all real numbers; intercepts: (0, -3) and (3, 0); a local maximum value of -2 is at -1; a local
Express the area A of an isosceles right triangle as a function of the length x of one of the two equal sides.
Redo Problem 89 with the following additional information: increasing on ( -∞, -1), (2, ∞); decreasing on (-1, 2). Again compare your graph with others and comment on any differences. Again
Express the gross salary G of a person who earns $10 per hour as a function of the number x of hours worked.
How many x-intercepts can a function defined on an interval have if it is increasing on that interval? Explain.
Tiffany, a commissioned salesperson, earns $100 base pay plus $10 per item sold. Express her gross salary G as a function of the number x of items sold.
Suppose that a friend of yours does not understand the idea of increasing and decreasing functions. Provide an explanation, complete with graphs, that clarifies the idea.
The functionrepresents the population P (in millions) of Americans that are a years of age or older.(a) Identify the dependent and independent variables.(b) Evaluate P(20). Provide a verbal
Can a function be both even and odd? Explain.
The functionrepresents the number N of housing units (in millions) that have r rooms, where r is an integer and 2 ¤ r ¤ 9.(a) Identify the dependent and independent
Using a graphing utility, graph y = 5 on the interval (-3, 3). Use MAXIMUM to find the local maximum values on (-3, 3). Comment on the result provided by the calculator.
If a rock falls from a height of 20 meters on Earth, the height H (in meters) after x seconds is approximatelyH(x) = 20 – 4.9x2(a) What is the height of the rock when x = 1 second?x = 1.1 seconds?
A function f has a positive average rate of change on the interval [2, 5]. Is f increasing on [2, 5] ? Explain.
If a rock falls from a height of 20 meters on the planet Jupiter, its height H (in meters) after x seconds is approximatelyH(x) = 20 -13x2(a) What is the height of the rock when x = 1 seconds?x = 1.1
Show that a constant function f(x) = b has an average rate of change of 0. Compute the average rate of change of y = √4 – x2 on the interval [-2, 2]. Explain how this can happen.
A Boeing 747 crosses the Atlantic Ocean (3000 miles) with an airspeed of 500 miles per hour. The cost C (in dollars) per passenger is given bywhere x is the ground speed(a) What is the cost per
The cross-sectional area of a beam cut from a log with radius 1 foot is given by the function a(x) = 4x√1 - x2, where x represents the length, in feet, of half the base of the beam. See the figure.
The participation rate is the number of people in the labor force divided by the civilian population (excludes military). Let L(x) represent the size of the labor force in year x and P(x) represent
Suppose that V(x) represents the number of violent crimes committed in year x and P(x)represents the number of property crimes committed in year x. Determine a function T that represents the combined
Suppose that P(x) represents the percentage of income spent on health care in year x and I(x)represents income in year x. Determine a function H that represents total health care expenditures in year
Suppose that I(x) represents the income of an individual in year x before taxes and T(x)represents the individual’s tax bill in year x. Determine a function N that represents the individual’s net
Suppose that the revenue R, in dollars, from selling x cell phones, in hundreds, is R(x) = - 1.2x2 + 220x. The cost C, in dollars, of selling x cell phones is C(x) = 0.05x3 – 2x2 + 65x + 500.(a)
Suppose that the revenue R, in dollars, from selling x clocks is R(x) = 30x. The cost C, in dollars, of selling x clocks is C(x) = 0.1 x2 + 7x + 400.(a) Find the profit function, P(x) = R(x) –
Find a function H that multiplies a number x by 3, then subtracts the cube of x and divides the result by your age.
The variable interest rate on a student loan changes each July 1 based on the bank prime loan rate. For the years 1992-2007, this rate can be approximated by the model r(x) = -0.115x2 + 1.183x +
(a) Find the distance from P1 = (-2, -3) to P2 = (3, -5).(b) What is the midpoint of the line segment from P1 to P2?(c) What is the slope of the line containing the points P1 and P2?
True or FalseEvery relation is a function.
Use the given graph of the function f to answer parts (a)(n).(a) Find f(0) and f(6).(b) Find f(2) and f(-2).(c) Is f(3)positive or negative?(d) Is f(-1) positive or negative?(e) For what
A circle of radius r is inscribed in a square. See the figure.(a) Express the area A of the square as a function of the radius r of the circle.(b) Express the perimeter p of the square as a function
True or FalseEven functions have graphs that are symmetric with respect to the origin.
In problem, find the domain of each function.f(x) = 3x2/x - 2
Graph each function using the techniques of shifting, compressing or stretching, and reflections. Start with the graph of the basic function and show all stages.(a) h(x) = -2(x + 1)3 + 3(b) g(x) = |x
In problem, solve each inequality. Graph the solution set.|4x + 1| ≥ 7
Use the given graph of the function f to answer parts (a)(n).(a) Find f(0) and f(-6).(b) Find f(6) and f(11).(c) Is f(3)positive or negative?(d) Is f(-4) positive or negative?(e) For what
A rectangle is inscribed in a circle of radius 2. See the figure. Let P = (x, y) be the point in quadrant I that is a vertex of the rectangle and is on the circle.(a) Express the area A of the
For the functions f(x) = 2x2 + 1 and g(x) = 3x - 2, find the following and simplify:(a) f - g(b) f ∙ g(c) f(x + h) - f(x)
In problem, solve each inequality. Graph the solution set.|2x - 5| < 3
If f(x) = x + 1 and g(x) = x3, then ______ = x3 – (x + 1).
The domain of f/g consists of numbers x for which g(x) _____ 0 that are in the domains of both _______ and _______.
True or FalseA function f is decreasing on an open interval I if, for any choice of x1 and x2 and in I, with x1 < x2, we have f(x1) > f(x2).
In problem, solve each inequality. Graph the solution set.2 – 3x > 6
True or FalseThe y-intercept of the graph of the function y = f(x), whose domain is all real numbers, is f(0).
A rectangle is inscribed in a semicircle of radius 2. See the figure. Let P = (x, y) be the point in quadrant I that is a vertex of the rectangle and is on the circle.(a) Express the area A of the
In problem, find the domain of each function.f(x) = x/x2 - 9
In problem, find the following for each function:(a) f(2)(b) f(-2)(c) f(-x)(d) -f(x)(e) f(x - 2)(f) (2x)f(x) = x3/x2 - 9
For the function f(x) = 3x2 – 3x + 4, find the average rate of change of f from 3 to 4.
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
True or FalseThe domain and the range of the reciprocal function are the set of all real numbers.
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 =
True or FalseThe graph of a function y = f(x) always crosses the y-axis.
A rectangle has one corner in quadrant I on the graph of y = 16 - x2, another at the origin, a third on the positive y-axis, and the fourth on the positive x-axis. See the figure.(a) Express the area
In problem, find the following for each function:(a) f(2)(b) f(-2)(c) f(-x)(d) -f(x)(e) f(x - 2)(f) (2x)f(x) = x2 – 4/x2
Consider the function(a) Graph the function.(b) List the intercepts.(c) Find f(-5).(d) Find g(2). f(x)= (2x+1 |x-4 x
True or FalseThe cube root function is odd and is decreasing on the interval (-∞, ∞).
True or FalseThe cube function is odd and is increasing on the interval (-∞, ∞).
The set of all images of the elements in the domain of a function is called the ________.
In problem, find the real solutions of each equation.√2x + 3 = 2
True or FalseA function can have more than one y-intercept.
A right triangle has one vertex on the graph of y = 9 - x2, x > 0, at (x, y), another at the origin, and the third on the positive x-axis at (x, 0). Express the area A of the triangle as a
A function f ________ is on an open interval I if, for any choice of x1 and x2 in I, with x1 > x2, we have f(x1) < f(x2).
In problem, find the following for each function:(a) f(2)(b) f(-2)(c) f(-x)(d) -f(x)(e) f(x - 2)(f) (2x)f(x) = |x2 – 4|
When functions are defined by more than one equation, they are called ________ functions.
If f is a function defined by the equation y = f(x)then x is called the ______ variable and y is the _________ variable.
In problem, find the real solutions of each equation.|2x + 3| = 4
True or FalseTo obtain the graph of f(x) = x3 + 5, shift the graph of y = x3 vertically up 5 units.
True or FalseTo obtain the graph of f(x) = √x + 2, shift the graph of y = √x horizontally to the right 2 units.
Aright triangle has one vertex on the graph of y = x3, x > 0. at (x, y) another at the origin, and the third on the positive y-axis at (0, y) as shown in the figure. Express the area A of the
The intercepts of the equation y = x2 – 9 are _______.
In problem, find the following for each function:(a) f(2)(b) f(-2)(c) f(-x)(d) -f(x)(e) f(x - 2)(f) (2x)f(x) = √x2 - 4
Using the graph of the function f:(a) Find the domain and the range of f.(b) List the intercepts.(c) Find f (1).(d) For what value(s) of x does f(x) = -3?(e) Solve f(x) < 0. УА 4F(1, 3) (0, 2),
Solve the inequality: 3 = 2x > 5. Graph the solution set.
In problem, find the real solutions of each equation.6x2 - 5x + 1 = 0
True or FalseThe graph of y = - f(x) is the reflection about the x-axis of the graph of y = f(x).
Let P = (x, y) be a point on the graph of y = 1/x.(a) Express the distance d from P to the origin as a function of x.(b) Use a graphing utility to graph d = d(x).(c) For what values of x is d
Write the point–slope form of the line with slope 5 containing the point (3, -2).
List the intercepts of the equation y = x3 - 8.
The slope of the line containing the points (-2, 3) and (3, 8) is _____.
In problem, determine whether each relation represents a function. For each function, state the domain and range.{(4, -1), (2, 1), (4, 2)}
Suppose that the graph of a function f is known. Then the graph of y = f(x - 2) may be obtained by a(n)________ shift of the graph of f to the a __________ distance of 2 units.
In problem, find the following for each function:(a) f(2)(b) f(-2)(c) f(-x)(d) -f(x)(e) f(x - 2)(f) (2x)f(x) = x2/x + 1
In problem, find the domain of each function and evaluate each function at x = -1.h(x) = x – 4/x2 + 5x - 36
The domain of the variable in the expression x – 3/x + 4 is________.
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