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college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

The length of a rectangle is 1 meter more than twice the width. If the rectangle’s area is 36 square meters, find its dimensions.
In Exercises 29–42, solve each system by the method of your choice. [3x² - 2y² = 1 4x - y = 3
In Exercises 25–35, solve each system by the method of your choice. [2x² + 3y² = 21 |3x² - 4y² = 23 2
What interest rate is required for an investment of $6000 subject to continuous compounding to grow to $18,000 in 10 years?
In Exercises 33–41, use the four-step strategy to solve each problem. Use x, y, and z to represent unknown quantities. Then translate from the verbal conditions of the problem to a system of three
Group members should choose a particular field of interest. Research how linear programming is used to solve problems in that field. If possible, investigate the solution of a specific practical
The bar graph shows the average age at which men in the United States married for the first time from 2009 through 2013. The data are displayed as five points in a scatter plot. Also shown is a line
In Exercises 39–52,a. Find an equation for f -1(x).b. Graph f and f -1 in the same rectangular coordinate system.c. Use interval notation to give the domain and the range of f and f -1.
In Exercises 51–66, finda. (f ° g)(x)b. (g ° f)(x)c. (f ° g)(2) f(x)=√x, g(x) = x + 2
In Exercises 45–52, use the graph of y = f(x) to graph each function g.g(x) = 1/2 f(x + 1) y = f(x) (-2,0) -5-4-3-2- y TI (0, 2) (2, 2) (4,0) 2 3 4 5 (-4,-2) |||| [III]?|IIIID X
In Exercises 51–54, graph the given square root functions, f and g, in the same rectangular coordinate system. Use the integer values of x given to the right of each function to obtain ordered
In Exercises 39–52,a. Find an equation for f -1(x).b. Graph f and f -1 in the same rectangular coordinate system.c. Use interval notation to give the domain and the range of f and f -1.
Use the graph of f to determine each of the following. Where applicable, use interval notation.a. The domain of fb. The range of fc. The x-interceptsd. The y-intercepte. Intervals on which f is
Use the graph of f to determine each of the following. Where applicable, use interval notation.a. The domain of fb. The range of fc. The x-interceptsd. The y-intercepte. Intervals on which f is
In Exercises 45–52, use the graph of y = f(x) to graph each function g.g(x) = 2f(x - 1) y = f(x) (-2,0) -5-4-3-2- y TI (0, 2) (2, 2) (4,0) 2 3 4 5 (-4,-2) |||| [III]?|IIIID X
Use the graph of f to determine each of the following. Where applicable, use interval notation.a. The domain of fb. The range of fc. The zeros of fd. F(0)e. Intervals on which f is increasingf.
In Exercises 55–59, use the graph of y = f(x) to graph each function g.g(x) = 1/2 f(x - 1) -4-3 N W 2- 1+ 2+ 2/3 4 y = f(x) X
In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation’s domain and range. (x + 2)² + y² = 16
In Exercises 53–66, begin by graphing the standard quadratic function, f(x) = x2. Then use transformations of this graph to graph the given function. g(x) = (x - 1)² 2
Graph: 2x - 10 = 0.
In Exercises 73–75, begin by graphing the cube root function, Then use transformations of this graph to graph the given function. f(x) = √x.
In Exercises 67–80, begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. h(x) = √x + 2
In Exercises 49–58, graph each equation in a rectangular coordinate system.x = -3
What explanations can you offer for the trends shown by the graph in Exercise 68?Data from Exercise 68A study of 900 working women in Texas showed that their feelings changed throughout the day. As
In Exercises 51–66, finda. (f ° g)(x)b. (g ° f)(x)c. (f ° g)(2)f(x) = 2x, g(x) = x + 7
In Exercises 65–70, use the graph of f to find each indicated function value.f(2) -5-4 30 T y y = f(x) 12 2.H HII A V DIDYFIZIID X
In Exercises 49–58, graph each equation in a rectangular coordinate system.f(x) = 1
In Exercises 60–63, begin by graphing the standard quadratic function, f(x) = x2. Then use transformations of this graph to graph the given function.g(x) = x2 + 2
In Exercises 93–94, let f(x) = x2 - x + 4 and g(x) = 3x - 5.Find g(1) and f (g(1)).
Describe how to write the equation of a line if the coordinates of two points along the line are known.
Fill in each blank so that the resulting statement is true.Consider the quadratic function f(x) = ax2 + bx + c, a ≠ 0. If a > 0, then f has a minimum that occurs at x =_______ . This minimum
In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree.f(x) = 7x2 + 9x4
In Exercises 17–24,a. List all possible rational roots.b. Use synthetic division to test the possible rational roots and find an actual root.c. Use the quotient from part (b) to find the remaining
Use the position functionto answer Exercises 75–76.Divers in Acapulco, Mexico, dive headfirst at 8 feet per second from the top of a cliff 87 feet above the Pacific Ocean. During which time period
In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph.f(x) = 4x
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents.4x = 32
Use the four-step procedure for solving variation problems given on page 445 to solve Exercises 21–36.Many people claim that as they get older, time seems to pass more quickly. Suppose that the
In Exercises 13–18, graph each equation in a rectangular coordinate system. If two functions are given, graph both in the same system. f(x) = |x and g(x) = |x|1
Use the four-step procedure for solving variation problems given on page 445 to solve Exercises 21–36.Radiation machines, used to treat tumors, produce an intensity of radiation that varies
In Exercises 19–24, use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function.f(x) = -11x4 - 6x2 + x + 3
In Exercises 15–18, use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with
The August 1978 issue of National Geographic described the 1964 find of bones of a newly discovered dinosaur weighing 170 pounds, measuring 9 feet, with a 6-inch claw on one toe of each hind foot.
In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. 1 In- 2 e
In Exercises 21–42, evaluate each expression without using a calculator. log₂ -100
In Exercises 25–34, begin by graphing f(x) = 2x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to
In Exercises 21–42, evaluate each expression without using a calculator. log6
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. logb x"y 2 Z
Use the formulasto solve this exercise. You decide to invest $8000 for 3 years at an annual rate of 8%. How much more is the return if the interest is compounded continuously than if it is compounded
In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log3 1 √3
In Exercises 21–26, complete the table. Round half-lives to one decimal place and values of k to six decimal places. Radioactive Substance Calcium-47 Half-Life 113 hours Decay Rate, k
In Exercises 25–34, begin by graphing f(x) = 2x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to
The function A = 82.3e-0.004t models the population of Germany, A, in millions, t years after 2010.a. What was the population of Germany in 2010?b. Is the population of Germany increasing or
Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to
The 2010 population of Asia was 4121 million; in 2050, it is projected to be 5231 million. Write the exponential growth function that describes the population of Asia, in millions, t years after 2010.
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. logs 64 Vx /x
In Exercises 23–25, write each expression as a single logarithm. 1 In x 3 In y ln(z − 2) -
In Exercises 21–26, complete the table. Round half-lives to one decimal place and values of k to six decimal places. Radioactive Substance Arsenic-74 Half-Life 17.5 days Decay Rate, k
In Exercises 25–34, begin by graphing f(x) = 2x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to
In Exercises 21–42, evaluate each expression without using a calculator. logs 1
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log6 36 √x
Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to
In Exercises 21–26, complete the table. Round half-lives to one decimal place and values of k to six decimal places. Radioactive Substance Uranium-238 Half-Life 4560 years Decay Rate, k
In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3*, g(x) = 3x-1, h(x) = 3x - 1, F(x) = -3*, G(x) = 3*, H(x)
Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to
In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason.ln e5
Use the compound interest formulas to solve Exercises 23–25.What interest rate, to the nearest tenth of a percent, is required for an investment subject to continuous compounding to double in 10
In Exercises 23–25, write each expression as a single logarithm.7 log5 x + 2 log5 x
In Exercises 21–42, evaluate each expression without using a calculator.log3 27
Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to
In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason.log17 17
If f(x) = x2 and g(x) = x + 2, find (f ° g)(x) and (g ° f)(x).
Use the exponential decay model, A = A0ekt, to solve this exercise. The half-life of iodine-131 is 7.2 days. How long will it take for a sample of this substance to decay to 30% of its original
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log X 2
In Exercises 25–34, begin by graphing f(x) = 2x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to
Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to
In Exercises 21–42, evaluate each expression without using a calculator. log3 -la
Shown, again, in the following table is world population, in billions, for seven selected years from 1950 through 2010. Using a graphing utility’s logistic regression option, we obtain the equation
The logistic growth functionmodels the percentage, P(x), of Americans who are x years old with some coronary heart disease. Use the function to solve Exercises 43–46.What percentage of
The figure shows the graph of f(x) = ex. In Exercises 35–46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine each
Graph f(x) = 4x and g(x) = log4 x in the same rectangular coordinate system.
In Exercises 30–33, determine whether the values in each table belong to an exponential function, a logarithmic function, a linear function, or a quadratic function. 0 1 2 3 4 y 3 1 -1 -3 -5
Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to
In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
In Exercises 41–43, find the domain of each logarithmic function.f(x) = log(3 - x)
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log V100x
Use the exponential decay model, A = A0ekt, to solve Exercises 28–31. Round answers to one decimal place.The half-life of lead is 22 years. How long will it take for a sample of this substance to
In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log 1 1000
The figure shows the graph of f(x) = ex. In Exercises 35–46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine each
The figure shows the graph of f(x) = ex. In Exercises 35–46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine each
The logistic growth functionmodels the percentage, P(x), of Americans who are x years old with some coronary heart disease. Use the function to solve Exercises 43–46.What percentage of
Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to
In Exercises 44–46, use inverse properties of logarithms to simplify each expression.ln e6x
In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
In Exercises 41–43, find the domain of each logarithmic function.f(x) = ln(x - 1)2
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
The figure shows the graph of f(x) = ex. In Exercises 35–46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine each
The logistic growth functionmodels the percentage, P(x), of Americans who are x years old with some coronary heart disease. Use the function to solve Exercises 43–46.At what age is the percentage
In Exercises 44–46, use inverse properties of logarithms to simplify each expression. 10log 4x²
In Exercises 44–46, use inverse properties of logarithms to simplify each expression. eln√x
Graph f(x) = (1/4)x and g(x) = log 1/4 x in the same rectangular coordinate system.

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