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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

Use transformations to sketch a graph of f. f(x) = -√1-x
Use transformations to sketch a graph of f. f(x) = -x² + 4
Use transformations to sketch a graph of f. x-^ = (x)f
Use transformations to sketch a graph of f. f(x) = |2x|
Use transformations to sketch a graph of f. Vx f(x)=1-√x
Use transformations to sketch a graph of f. f(x)= x + 2-3
Use transformations to sketch a graph of f. f(x) = √-x-1
Use transformations to sketch a graph of f. f(x) = = |x|
Use transformations to sketch a graph of f. f(x) = 2√x-2-1
Use transformations to sketch a graph of f. f(x) = (x - 1)³
Use transformations to sketch a graph of f. f(x) = √(x + 1) V-(x
Use transformations to sketch a graph of f. f(x) = -x³
Use transformations to sketch a graph of f. f(x) = 2 + V-(x − 3)
Two functions, f and g, are related by the given equation. Use the numerical representation of f to make a numerical representation of g. g(x) = f(x) + 7 1 5 X f(x) 2 1 3 6 4 2 5 7 6 9
Use transformations to sketch a graph of f. f(x) = (x + 2)³
Two functions, f and g, are related by the given equation. Use the numerical representation of f to make a numerical representation of g. g(x) = f(x - 2) X -4 5 f(x) -2 2 0 -3 2 -5 4 -9
Two functions, f and g, are related by the given equation. Use the numerical representation of f to make a numerical representation of g. g(x) = f(x + 50) x-100 f(x) 25 -50 0 80 120 50 100 150 100
Use transformations to sketch a graph of f. f(x) = (-x)³ + 1
Two functions, f and g, are related by the given equation. Use the numerical representation of f to make a numerical representation of g. g(x) = f(x 3) + 5 f(x) -3 3 0 00 8 3 15 6 27 9 31
Two functions, f and g, are related by the given equation. Use the numerical representation of f to make a numerical representation of g. g(x) = f(x) = 10 X f(x) 0 -5 5 11 10 21 15 32 20 47
Two functions, f and g, are related by the given equation. Use the numerical representation of f to make a numerical representation of g. g(x) = f(-x) + 1 x -2 -1 11 8 f(x) 0 0 5 1 2 2 -1
Two functions, f and g, are related by the given equation. Use the numerical representation of f to make a numerical representation of g. g(x) = f(x + 1) - 2 X f(x) 1 2 2 4 3 3 4 7 5 8 00 6 10
If a circle has an area that is 225π square feet or more, what are the possible diameters d for the circle?
The points (-12, 6), (0, 8), and (8,-4) lie on the graph of y = f(x). Determine three points that lie on the graph of y = g(x). g(x) = f(x) + 2
The points (-12, 6), (0, 8), and (8,-4) lie on the graph of y = f(x). Determine three points that lie on the graph of y = g(x). g(x) = f(x) - 3
Two functions, f and g, are related by the given equation. Use the numerical representation of f to make a numerical representation of g. g(x) = −f(x + 2) -2 8 X-4 5 f(x) 0 10 2 8 4 5
The points (-12, 6), (0, 8), and (8,-4) lie on the graph of y = f(x). Determine three points that lie on the graph of y = g(x). g(x) = f(x - 2) + 1
The points (-12, 6), (0, 8), and (8,-4) lie on the graph of y = f(x). Determine three points that lie on the graph of y = g(x). g(x) = -f(x)
The points (-12, 6), (0, 8), and (8,-4) lie on the graph of y = f(x). Determine three points that lie on the graph of y = g(x). g(x) = f(x + 1) - 1
The points (-12, 6), (0, 8), and (8,-4) lie on the graph of y = f(x). Determine three points that lie on the graph of y = g(x). g(x) = f(-2x)
The points (-12, 6), (0, 8), and (8,-4) lie on the graph of y = f(x). Determine three points that lie on the graph of y = g(x). g(x) = f(-x)
Let the domain of f(x) be [-1, 2] and the range be [0, 3]. Find the domain and range of the following. 5f(x + 1)
The points (-12, 6), (0, 8), and (8,-4) lie on the graph of y = f(x). Determine three points that lie on the graph of y = g(x). (x) ft-=(x)
Let the domain of f(x) be [-1, 2] and the range be [0, 3]. Find the domain and range of the following. -f(x)
Let the domain of f(x) be [-1, 2] and the range be [0, 3]. Find the domain and range of the following. f(x-3) + 1
Let the domain of f(x) be [-1, 2] and the range be [0, 3]. Find the domain and range of the following. f(x - 2)
Let the domain of f(x) be [-1, 2] and the range be [0, 3]. Find the domain and range of the following. -2f(-x)
Let the domain of f(x) be [-1, 2] and the range be [0, 3]. Find the domain and range of the following. f(2x)
Let the domain of f(x) be [-1, 2] and the range be [0, 3]. Find the domain and range of the following. 2f(x - 1)
Let the domain of f(x) be [-1, 2] and the range be [0, 3]. Find the domain and range of the following. f(-x)
Determine the domain and range of function f. Use interval notation. f(x) = −(x + 1)² = 5 -
Determine the domain and range of function f. Use interval notation. f(x) = 2(x - 5)² + 10.
Use transformations of graphs to model the table of data with the formula f(x) = a(x - h)2 + k.Cumulative number of apps downloaded from the Apple store (billions). Year 2010 2011 2012 2013 2014 Apps
Determine the domain and range of function f. Use interval notation. f(x) = V-x-4-2
Determine the domain and range of function f. Use interval notation. f(x) = -√x-1+3
Use transformations of graphs to model the table of data with the formula f(x) = a(x - h)2 + k.Number of iPhones sold (millions) Year 2009 2010 2014 2015 iPhones 20.7 40.0 169 231
Use transformations of graphs to model the table of data with the formula f(x) = a(x - h)2 + k.Google revenue ($ billions) Year 2008 2009 2010 24 29 Revenue 22 2014 2015 66 75
Use transforma- tions of graphs to model the table of data with the formula f(x) = a(x - h)2 + k.Average price of a home in thousands of dollars Year 1970 1980 1990 Price 30 80 150 2000 210 2005 300
The general trend in the percentage P of homes lived in by owners rather than renters is modeled by P(x) = 0.00075x2 + 0.17x + 44, where x is years after 1990. Determine a function g that computes P,
The function D defined by D(x) = 2375x2 + 5134x + 5020 models AIDS deaths x years after 1984. Write a formula g(x) that computes AIDS deaths during year .x, where x is the actual year.
Suppose that the airplane in FIGURE 3.97 is flying at 0.2 kilometer per second to the left, rather than to the right. If the position of the airplane is fixed at (-1, 5), graph the image of the
Suppose that the airplane in FIGURE 3.97 is traveling to the right at 0.1 kilometer per second and gaining altitude at 0.05 kilometer per second. If the airplane's position is fixed at (-1, 5), graph
Suppose a cold front passing through the United States at noon, has a shape described by the function y = 1/20x2. Each unit represents 100 miles. Des Moines, Iowa, is located at (0, 0), and the
The first figure at the top of the next column is a picture composed of lines and curves. In this exercise we will model only the red semicircle that outlines the top of the silo. In order to make it
Computer graphics frequently use reflections. Reflections can speed up the generation of a picture or create a figure that appears perfectly symmetrical.(a) For the given f(x), constant k, and
Computer graphics frequently use reflections. Reflections can speed up the generation of a picture or create a figure that appears perfectly symmetrical.(a) For the given f(x), constant k, and
Computer graphics frequently use reflections. Reflections can speed up the generation of a picture or create a figure that appears perfectly symmetrical.(a) For the given f(x), constant k, and
Computer graphics frequently use reflections. Reflections can speed up the generation of a picture or create a figure that appears perfectly symmetrical.(a) For the given f(x), constant k, and
Explain how to graph the reflection of y = f(x) across the x-axis. Give an example.
Let e be a positive number. Explain how to shift the graph of y = f(x) upward, downward, left, or right e units. Give examples.
If the graph of y = f(x) undergoes a vertical stretch or shrink to become the graph of y = g(x), do these two graphs have the same x-intercepts? y-intercepts? Explain your answers.
If the graph of y = f(x) undergoes a horizontal stretch or shrink to become the graph of y = g(x). do these two graphs have the same x-intercepts? y-intercepts? Explain your answers.
In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius.Center (-1, 4), r = 2
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.a.b.c. f(r) = √25 r - 6 -
In Exercises 33–34, find and simplify the difference quotientf(x) = -2x2 + x + 10 f(x + h) − f(x)¸ h ‡ 0 h
In Exercises 33–44, use the graph of y = f(x) to graph each function g.g(x) = f(x) - 2 -4,0) -5-4-3 4-33 y = f(x) y (0,0) 2- 3.4 45 -2) (4-2) X
Which graphs in Exercises 29–34 represent functions that have inverse functions? y X
In Exercises 33–36, use possible symmetry to determine whether each graph is the graph of an even function, an odd function, or a function that is neither even nor odd. +32 + NA (-4,-1) y 4-3-2-11-
The graph shows the height, in meters, of an eagle in terms of its time, in seconds, in flight.a. Is the eagle’s height a function of time? Use the graph to explain why or why not.b. On which
In Exercises 27–38, graph each equation in a rectangular coordinate system.f(x) = x - 4
In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius.Center (2, -1), r = 4
Express h(x) = (2x + 3)7 as a composition of two functions f and g so that h(x) = (f ° g)(x).
A formula in the form y = mx + b models the average retail price, y, of a new car x years after 2000. Would you expect m to be positive, negative, or zero? Explain your answer.
In Exercises 31–50, find f + g, f - g, fg, and f/g. Determine the domain for each function.f(x) = x - 6, g(x) = 5x2
In Exercises 33–36, use possible symmetry to determine whether each graph is the graph of an even function, an odd function, or a function that is neither even nor odd. H (+1,1) -4-3- III 432
In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Passing through (-2, -5) and (6, -5)
Find the length and the midpoint of the line segment whose endpoints are (2, -2) and (5, 2).
In Exercises 27–38, graph each equation in a rectangular coordinate system.f(x) = |x| - 4
What is a secant line?
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.a.b.c. f(x) = 4x³ + 1 +3
Use the graph of y = f(x) to solve this exercise.a. What are the zeros of f ?b. Find the value(s) of x for which f(x) = -1.c. Find the value(s) of x for which f(x) = -2.d. Is f even, odd, or
Use the graph of y = f(x) to solve Exercises 1–5.For what value(s) of x is f(x) = 1? y -3- -4-3-2-1-1 1 {y = f(x) H 34 IIDIID X
In Exercises 33–36, use possible symmetry to determine whether each graph is the graph of an even function, an odd function, or a function that is neither even nor odd. y HINA (1,3)
In Exercises 31–50, find f + g, f - g, fg, and f/g. Determine the domain for each function.f(x) = 2x2 - x - 3, g(x) = x + 1
In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Passing through (2, 4) with x-intercept = -2
A cargo service charges a flat fee of $5 plus $1.50 for each pound or fraction of a pound. Graph shipping cost, C(x), in dollars, as a function of weight, x, in pounds, for 0 < x ≤ 5.
Use the graph of y = f(x) to solve Exercises 1–5.Find the domain and the range of f. y -3- -4-3-2-1-1 1 {y = f(x) H 34 IIDIID X
In Exercises 27–38, graph each equation in a rectangular coordinate system.5y = -3x
Use the graph of y = f(x) to solve Exercises 1–5.Find the relative maximum. y -3- -4-3-2-1-1 1 {y = f(x) H 34 IIDIID X
In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius.Center (-3, 5), r = 3
Use the graph of y = f(x) to solve this exercise.a. What is f(4) - f(-3)?b. What is the domain of f ?c. What is the range of f ?d. On which interval or intervals is f increasing?e. On which interval
Use the graph of y = f(x) to solve Exercises 1–5.Graph g(x) = f(x - 1) + 1. y -3- -4-3-2-1-1 1 {y = f(x) H 34 IIDIID X
Use the graph of y = f(x) to solve Exercises 1–5.Graph h(x) = -2f(1/2x). y -3- -4-3-2-1-1 1 {y = f(x) H 34 IIDIID X
In Exercises 1–3, determine whether each relation is a function. Give the domain and range for each relation.{(2, 7), (3, 7), (5, 7)}
In Exercises 1–3, determine whether each relation is a function. Give the domain and range for each relation.{(1, 10), (2, 500), (13, π)}
In Exercises 1–12, use the graph to determinea. Intervals on which the function is increasing, if any.b. Intervals on which the function is decreasing, if any.c. Intervals on which the function is
In Exercises 4–6, determine whether each equation defines y as a function of x.2x + y = 8
In Exercises 1–3, determine whether each relation is a function. Give the domain and range for each relation.{(12, 13), (14, 15), (12, 19)}
In Exercises 4–15, graph each equation in a rectangular coordinate system. If two functions are indicated, graph both in the same system. Then use your graphs to identify each relation’s domain
In Exercises 4–15, graph each equation in a rectangular coordinate system. If two functions are indicated, graph both in the same system. Then use your graphs to identify each relation’s domain

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