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mathematics
college algebra graphs and models
Questions and Answers of
College Algebra Graphs And Models
Divide the expression. 5x(3x² - 6x + 1) 3x²
The graph and degree of a polynomial with real coefficients f(x) are given. Determine the number of real zeros and the number of nonreal complex zeros. Assume that all zeros of f(x) are distinct.
These exercises investigate the relationship between polynomial functions and their average rates of change. For example, the average rate of change of f(x) = x2 from x to x + 0.001 for any x can be
Determine whether f is a rational function and state its domain. f(x) = ± +1
Find any vertical or horizontal asymptotes for the graph ofState the domain of f. 4x² x² f(x): =-
Use the given zeros to write the complete factored form of f(x). f(x) = x³ = 2x² - 5x + 6; zeros: -2, 1, and 3
Determine if the function is a polynomial function. If it is, state its degree and leading coefficient a. f(x) = 5 - 4x
Use the given zeros to write the complete factored form of f(x). f(x) = 6x² + 21x = 90; zeros: -6 and -
Divide the expression. 2x43x² + 4x - 7
These exercises investigate the relationship between polynomial functions and their average rates of change. For example, the average rate of change of f(x) = x2 from x to x + 0.001 for any x can be
The graph and degree of a polynomial with real coefficients f(x) are given. Determine the number of real zeros and the number of nonreal complex zeros. Assume that all zeros of f(x) are distinct.
Use the graph of the polynomial function f to complete the following. Let a be the leading coefficient of the polynomial f(x). (a) Determine the number of turning points and estimate any
Solve the rational equation (a) Symbolically, (b) Graphically, and (c) Numerically. 1 I+x 1 x-1 1
Determine whether f is a rational function and state its domain. f(x) |x-1| x + 1
Sketch a graph of f(x) = -x(x + 1)2 by hand and identify the x- and y-intercepts.
In Exercises 95–96, let f and g be defined by the following table: x -2 -1 0 1 2 f(x) 6 3 -1 -4 0 g(x) 0 4 1 -3 -6
Show thatis its own inverse. f(x) 3x - 2 5r – 3
A telephone company offers the following plans. Also given are the piecewise functions that model these plans. Use this information to solve Exercises 95–96.Plan A• $30 per month buys 120
Which graphs in Exercises 96–99 represent functions that have inverse functions? -4-3-2 -2-1 y -3- .............. 2.3 (DP²³▬ICIO TH X
In Exercises 95–106, begin by graphing the standard cubic function, f(x) = x3. Then use transformations of this graph to graph the given function. g(x) = x³ - 2
Find the area of the donut-shaped region bounded by the graphs of (x - 2)2 + (y + 3)2 = 25 and (x - 2)2 + (y + 3)2 = 36.
In Exercises 95–96, find all values of x satisfying the given conditions.f(x) = 1 - 2x, g(x) = 3x2 + x - 1, and (f ° g)(x) = -5.
Explain how to graph the equation x = 2. Can this equation be expressed in slope-intercept form? Explain.
Exercises 101–103 will help you prepare for the material covered in the first section of the next chapter.0 = -2(x - 3)2 + 8
In Exercises 101–102, find an equation for f -1(x). Then graph f and f -1 in the same rectangular coordinate system.f(x) = 1 - x2, x ≥ 0
The bar graph shows the population of the United States, in millions, for seven selected years. Here are two functions that model the data:Use the functions to solve Exercises 97–98.a. Write a
The bar graph shows the population of the United States, in millions, for seven selected years. Here are two functions that model the data:Use the functions to solve Exercises 97–98.a. Write a
Which graphs in Exercises 96–99 represent functions that have inverse functions? H 4-3-2 y ॐ प्रै Afx X
In Exercises 95–106, begin by graphing the standard cubic function, f(x) = x3. Then use transformations of this graph to graph the given function. g(x) = (x 3)
In Exercises 97–98, find f(-x) - f(x) for the given function f. Then simplify the expression.f(x) = x3 + x - 5
In Exercises 95–106, begin by graphing the standard cubic function, f(x) = x3. Then use transformations of this graph to graph the given function. g(x) = (x - 2)³
A tangent line to a circle is a line that intersects the circle at exactly one point. The tangent line is perpendicular to the radius of the circle at this point of contact. Write an equation in
Which graphs in Exercises 96–99 represent functions that have inverse functions? -10 -3-2- y П X
Divide and express the result in standard form: 4i + 7 5 - 2i
In Exercises 97–98, write a piecewise function that models each telephone billing plan. Then graph the function.$50 per month buys 400 minutes. Additional time costs $0.30 per minute.
Freedom 7 was the spacecraft that carried the first American into space in 1961. Total flight time was 15 minutes and the spacecraft reached a maximum height of 116 miles. Consider a function, s,
A company that sells radios has yearly fixed costs of $600,000. It costs the company $45 to produce each radio. Each radio will sell for $65. The company’s costs and revenue are modeled by the
Solve and determine whether the equation 7(x - 2) + 5 = 7x - 9 is an identity, a conditional equation, or an inconsistent equation.
Explain how to use the general form of a line’s equation to find the line’s slope and y-intercept.
In Exercises 97–98, find f(-x) - f(x) for the given function f. Then simplify the expression.f(x) = x2 - 3x + 7
The Corruption Perceptions Index uses perceptions of the general public, business people, and risk analysts to rate countries by how likely they are to accept bribes. The ratings are on a scale from
If f(2) = 6, and f is one-to-one, find x satisfying 8 + f -1(x - 1) = 10.
In Exercises 95–106, begin by graphing the standard cubic function, f(x) = x3. Then use transformations of this graph to graph the given function. EX- x = (x)y
In Exercises 97–98, write a piecewise function that models each telephone billing plan. Then graph the function.$60 per month buys 450 minutes. Additional time costs $0.35 per minute.
Which graphs in Exercises 96–99 represent functions that have inverse functions? -4-3- -2- HIIHII X
The Corruption Perceptions Index uses perceptions of the general public, business people, and risk analysts to rate countries by how likely they are to accept bribes. The ratings are on a scale from
Explain how to use intercepts to graph the general form of a line’s equation.
With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises
Use the graph of f in the figure shown to draw the graph of its inverse function. -4-3-2 32 y 3- -3- y = f(x) 2 3 4 X
In Exercises 95–106, begin by graphing the standard cubic function, f(x) = x3. Then use transformations of this graph to graph the given function. h(x) = (x - 2)² 3
With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises
The bar graph shows your chances of surviving to various ages once you reach 60.The functionsmodel the chance, as a percent, that a 60-year-old will survive to age x. Use this information to solve
Take another look at the scatter plot in Exercise 91. Although there is a relationship between literacy and child mortality, we cannot conclude that increased literacy causes child mortality to
Solve and graph the solution set on a number line: -9 ≤ 4x - 1 < 15.
In Tom Stoppard’s play Arcadia, the characters dream and talk about mathematics, including ideas involving graphing, composite functions, symmetry, and lack of symmetry in things that are tangled,
A department store has two locations in a city. From 2012 through 2016, the profits for each of the store’s two branches are modeled by the functions f(x) = -0.44x + 13.62 and g(x) = 0.51x + 11.14.
Use a graphing utility to graph each equation in Exercises 100–103.Then use the .Trace. feature to trace along the line and find the coordinates of two points. Use these points to compute the
In Exercises 95–106, begin by graphing the standard cubic function, f(x) = x3. Then use transformations of this graph to graph the given function. h(x) = x³
Use a graphing utility to graph each equation in Exercises 100–103.Then use the .Trace. feature to trace along the line and find the coordinates of two points. Use these points to compute the
With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises
The bar graph shows your chances of surviving to various ages once you reach 60.The functionsmodel the chance, as a percent, that a 60-year-old will survive to age x. Use this information to solve
In Exercises 101–102, find an equation for f -1(x). Then graph f and f -1 in the same rectangular coordinate system. f(x) = √x + 1
Use a graphing utility to graph each equation in Exercises 100–103.Then use the .Trace. feature to trace along the line and find the coordinates of two points. Use these points to compute the
In Exercises 95–106, begin by graphing the standard cubic function, f(x) = x3. Then use transformations of this graph to graph the given function. h(x) = x³ 4
Exercises 103–105 will help you prepare for the material covered in the next section. Let (x1, y₁) = (7,2) and (x2, Y2) (1, -1). Find √(x₂ − x₁)² + (y₂ − y₁)². Express the answer
The wage gap is used to compare the status of women’s earnings relative to men’s. The wage gap is expressed as a percent and is calculated by dividing the median, or middlemost, annual earnings
Exercises 101–103 will help you prepare for the material covered in the first section of the next chapter.-x2 - 2x + 1 = 0
Use a graphing utility to graph each equation in Exercises 100–103.Then use the .Trace. feature to trace along the line and find the coordinates of two points. Use these points to compute the
With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises
The regular price of a computer is x dollars. Let f(x) = x - 400 and g(x) = 0.75x.a. Describe what the functions f and g model in terms of the price of the computer.b. Find (f ° g)(x) and describe
Is there a relationship between wine consumption and deaths from heart disease? The table gives data from 19 developed countries.a. Use the statistical menu of your graphing utility to enter the 19
Solve and graph the solution set on a number line:3|2x - 1 ≥ 21.
In Exercises 95–106, begin by graphing the standard cubic function, f(x) = x3. Then use transformations of this graph to graph the given function. r(x) = (x 3)³ + 2
Exercises 101–103 will help you prepare for the material covered in the first section of the next chapter.Use the graph of f(x) = x2 to graph g(x) = (x + 3)2 + 1.
The regular price of a pair of jeans is x dollars. Let f(x) = x - 5 and g(x) = 0.6x.a. Describe what functions f and g model in terms of the price of the jeans.b. Find (f ° g)(x) and describe what
The wage gap is used to compare the status of women’s earnings relative to men’s. The wage gap is expressed as a percent and is calculated by dividing the median, or middlemost, annual earnings
With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises
With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises
In Exercises 95–106, begin by graphing the standard cubic function, f(x) = x3. Then use transformations of this graph to graph the given function. r(x) = (x - 2) + 1
In Exercises 103–104, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places.(-2, 3) and (3, -9)
With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises
If a function is defined by an equation, explain how to find its domain.
Use a rectangular coordinate system to graph the circle with center (1, -1) and radius 1.
In Exercises 103–104, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places.(-4, 3) and (-2, 5)
If equations for f and g are given, explain how to find f - g.
Solve by completing the square: y2 - 6y - 4 = 0.
If equations for two functions are given, explain how to obtain the quotient function and its domain.
A company that manufactures bicycles has a fixed cost of $100,000. It costs $100 to produce each bicycle. The total cost for the company is the sum of its fixed cost and variable costs. Write the
In Exercises 105–108, determine whether each statement makes sense or does not make sense, and explain your reasoning.The graph of my linear function at first increased, reached a maximum point,
In Exercises 95–106, begin by graphing the standard cubic function, f(x) = x3. Then use transformations of this graph to graph the given function. h(x)=1/(x-3)³ - 2
In Exercises 105–106, find the midpoint of each line segment with the given endpoints.(2, 6) and (-12, 4)
With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises
Describe a procedure for finding (f ° g)(x). What is the name of this function?
Here is the Federal Tax Rate Schedule X that specifies the tax owed by a single taxpayer for a recent year.The preceding tax table can be modeled by a piecewise function, where x represents the
In Exercises 95–106, begin by graphing the standard cubic function, f(x) = x3. Then use transformations of this graph to graph the given function. h(x) = (x - 2)³ - 1
Here is the Federal Tax Rate Schedule X that specifies the tax owed by a single taxpayer for a recent year.The preceding tax table can be modeled by a piecewise function, where x represents the
In Exercises 105–108, you will be developing functions that model given conditions.You commute to work a distance of 40 miles and return on the same route at the end of the day. Your average rate
In Exercises 105–108, you will be developing functions that model given conditions.A car was purchased for $22,500. The value of the car decreased by $3200 per year for the first six years. Write a
In Exercises 105–106, find the midpoint of each line segment with the given endpoints.(4, -6) and (-15, 2)
In Exercises 107–118, begin by graphing the cube root function, f(x) = 3√x. Then use transformations of this graph to graph the given function. g(x)=√x + 2
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