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college algebra graphs and models
College Algebra 7th Edition Robert F Blitzer - Solutions
Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 0 (9-x)(x - t)x
Given f(x) = 2x3 - 7x2 + 9x - 3, use the Remainder Theorem to find f(-13).
In Exercises 21–36, find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. g(x) || ₁ x - 5 1²-25
In Exercises 25–32, find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero.f(x) = x3 + 5x2 - 9x - 45
In Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola’s axis of symmetry. Use the graph to determine the function’s domain and range.f(x) = x2 + 3x - 10
Use the four-step procedure for solving variation problems given on page 445 to solve Exercises 21–36.The water temperature of the Pacific Ocean varies inversely as the water’s depth. At a depth of 1000 meters, the water temperature is 4.4° Celsius. What is the water temperature at a depth of
In Exercises 25–32, find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. n = 3; 6 and -5 + 2i are zeros; f(2) = -636
Fill in each blank so that the resulting statement is true.The function f(x) = logb x is the_______ function with base______ .
In Exercises 1–5, graph f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. Give each function’s domain and range.f(x) = 2x and g(x) = 2x - 3
Graph f(x) = 2x and g(x) = 2x+1 in the same rectangular coordinate system.
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. logg (13.7)
Fill in each blank so that the resulting statement is true. The exponential function f with base b is defined by f(x) = _______, b > 0 and b ≠ 1. Using interval notation, the domain of this function is________ and the range is_________ .
Fill in each blank so that the resulting statement is true.If 24x-1 = 27, then_______ = 7.
Fill in each blank so that the resulting statement is true.The quotient rule for logarithms states that logb (M/N) =_______ . The logarithm of a quotient is the_________ of the logarithms.
Fill in each blank so that the resulting statement is true.For each of the scatter plots in Exercises 4–6, determine whether an exponential function, a logarithmic function, or a linear function is the best choice for modeling the data._________ . y
Fill in each blank so that the resulting statement is true.logb bx =________
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places.4-1.5
In Exercises 1–8, solve each equation or inequality.log2(x + 5) + log2(x - 1) = 4
Fill in each blank so that the resulting statement is true.For each of the scatter plots in Exercises 4–6, determine whether an exponential function, a logarithmic function, or a linear function is the best choice for modeling the data.________ . y
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents.22x-1 = 32
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places.6-1.2
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents.32x+1 = 27
In Exercises 1–8, solve each equation or inequality.ln(x + 4) + ln(x + 1) = 2 ln(x + 3)
In Exercises 1–8, write each equation in its equivalent exponential form. 3 = log, 27
Fill in each blank so that the resulting statement is true.The graph of f(x) = logb x approaches, but does not touch, the________ -axis. This axis, whose equation is________ , is a/an_________ asymptote.
Fill in each blank so that the resulting statement is true.Consider the compound interest formula This formula gives the balance,________ , in an account with principal________ and annual interest rate_________ , in decimal form, subject to compound interest paid______ times per year. = P(1. A =
In Exercises 1–4, the graph of an exponential function is given. Select the function for each graph from the following options:f(x) = 4x, g(x) = 4-x,h(x) = -4-x, r(x) = -4-x + 3. x
In Exercises 1–8, write each equation in its equivalent exponential form. 2 = logg x
The exponential models describe the population of the indicated country, A, in millions, t years after 2010. Use these models to solve Exercises 1–6.Which countries have a decreasing population? By what percentage is the population of these countries decreasing each year?
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(1000x)
In Exercises 1–8, solve each equation or inequality.e5x - 32 = 96
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents.5x = 625
In Exercises 1–5, graph f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. Give each function’s domain and range.f(x) = log2 x and g(x) = log2(x - 1) + 1
Write in logarithmic form: √36 = 6.
The exponential models describe the population of the indicated country, A, in millions, t years after 2010. Use these models to solve Exercises 1–6.When will India’s population be 1377 million? India Iraq Japan Russia A = 1173.1e0.008t A = 31.5e0.019r A = 127.3e-0.006t A = 141.9e0.00: -0.005t
Fill in each blank so that the resulting statement is true.If compound interest is paid twice a year, we say that the interest is compounded__________ . If compound interest is paid four times a year, we say that the interest is compounded__________ . If the number of compounding periods increases
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(10,000x)
In Exercises 1–8, write each equation in its equivalent exponential form. 5 = logb 32
Fill in each blank so that the resulting statement is true.If then________ = x - 3. In 7x23 x + 1 = ln(x - 3),
The exponential models describe the population of the indicated country, A, in millions, t years after 2010. Use these models to solve Exercises 1–6.When will India’s population be 1491 million? India Iraq Japan Russia A = 1173.1e0.008t A = 31.5e0.019r A = 127.3e-0.006t A = 141.9e0.00: -0.005t
Fill in each blank so that the resulting statement is true.If log5(x + 1) = 3, then_______ = x + 1.
In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function’s domain and range.f(x) = 2x and g(x) = 2x-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. log 7 X
About the size of New Jersey, Israel has seen its population soar to more than 6 million since it was established. The graphs show that by 2050, Palestinians in the West Bank, Gaza Strip, and East Jerusalem will outnumber Israelis. Exercises 7–8 involve the projected growth of these two
Find the domain: f(x) = ln(3 - x).
Fill in each blank so that the resulting statement is true.If log3 x + log3(x + 1) = 2, then log3 _______ = 2.
Fill in each blank so that the resulting statement is true.blogb x =______
In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function’s domain and range.f(x) = 3x and g(x) = 3x - 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. logo 9 X
In Exercises 6–7, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log3 √x 81
In Exercises 6–9, find the domain of each function.f(x) = log3(x + 6)
In Exercises 6–7, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.log4(64x5)
In Exercises 1–8, write each equation in its equivalent exponential form. log6 216 = y
About the size of New Jersey, Israel has seen its population soar to more than 6 million since it was established. The graphs show that by 2050, Palestinians in the West Bank, Gaza Strip, and East Jerusalem will outnumber Israelis. Exercises 7–8 involve the projected growth of these two
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents.42x-1 = 64
In Exercises 1–8, solve each equation or inequality.14 - 5x ≥ -6
In Exercises 1–8, solve each equation or inequality. |2x - 4 ≤ 2
In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function’s domain and range. g(x) and g(x) = ()* f(x) = ()* and
Fill in each blank so that the resulting statement is true.Using interval notation, the domain of f(x) = logb x is______ and the range is_______ .
Fill in each blank so that the resulting statement is true.y = 3(5)x can be written in terms of base e as y = 3e(__).x.______
In Exercises 6–9, find the domain of each function.g(x) = log3 x + 6
In Exercises 1–8, write each equation in its equivalent exponential form. log5 125 = y
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places.e-3.4
True or false: x4 = 15 is an exponential equation.________
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents.53x-1 = 125
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 100
In Exercises 6–9, find the domain of each function.h(x) = log3(x + 6)2
In Exercises 8–9, write each expression as a single logarithm.6 log x + 2 log y
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places.e-0.95
Fill in each blank so that the resulting statement is true.True or false: 4x = 15 is an exponential equation.________
In Exercises 9–14, graph each equation in a rectangular coordinate system. If two functions are indicated, graph both in the same system.(x - 3)2 + (y + 2)2 = 4
Fill in each blank so that the resulting statement is true.The graph of g(x) = 5 + log2 x is the graph of f(x) = log2 x shifted________ .
In Exercises 1–4, the graph of an exponential function is given. Select the function for each graph from the following options:f(x) = 4x, g(x) = 4-x,h(x) = -4-x, r(x) = -4-x + 3. y ... X
In Exercises 1–8, solve each equation or inequality. V2x5Vx3 = 1
Fill in each blank so that the resulting statement is true.In the model for exponential growth or decay, the amount, or size, at t = 0 is represented by_______ . The amount, or size, at time t is represented by_______ .
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places.32.4
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents.3x = 81
The exponential models describe the population of the indicated country, A, in millions, t years after 2010. Use these models to solve Exercises 1–6.What was the population of Iraq in 2010? India Iraq Japan Russia A = 1173.1e0.008t A = 31.5e0.019r A = 127.3e-0.006t A = 141.9e0.00: -0.005t
In Exercises 1–8, write each equation in its equivalent exponential form. 6 = log₂ 64
In Exercises 1–5, graph f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. Give each function’s domain and range. f(x) = (¹)* and g(x) = ( ¹ )x−¹ x-1
Fill in each blank so that the resulting statement is true.The graph of the exponential function f with base b approaches, but does not touch, the_______ -axis. This axis, whose equation is________ , is a/an________ asymptote.
Graph f(x) = log2 x and g(x) = log2(x - 1) in the same rectangular coordinate system.
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. log7(7x)
Fill in each blank so that the resulting statement is true.If x ln 9 = ln 20, then x =_______ .
Fill in each blank so that the resulting statement is true.The power rule for logarithms states that logb Mp =_______ . The logarithm of a number with an exponent is the________ of the exponent and the logarithm of that number.
Fill in each blank so that the resulting statement is true.Consider the model for limited logistic growth given by The amount, or size, at time t is represented by_____ . This value can never exceed________ . A = C 1 + ae-bt*
Fill in each blank so that the resulting statement is true.logb b =_______ .
In Exercises 1–4, the graph of an exponential function is given. Select the function for each graph from the following options:f(x) = 4x, g(x) = 4-x,h(x) = -4-x, r(x) = -4-x + 3. 2 y TT www X
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places.3√5
In Exercises 1–8, solve each equation or inequality.x4 + x3 - 3x2 - x + 2 = 0
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents.5x = 125
In Exercises 1–8, write each equation in its equivalent exponential form. 2 = log3 x
The exponential models describe the population of the indicated country, A, in millions, t years after 2010. Use these models to solve Exercises 1–6.Which country has the greatest growth rate? By what percentage is the population of that country increasing each year? India Iraq Japan Russia A =
Fill in each blank so that the resulting statement is true.The value that approaches as n gets larger and larger is the irrational number_______ , called the________ base. This irrational number is approximately equal to________ . 1 + 1 n n
In Exercises 1–5, graph f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. Give each function’s domain and range.f(x) = ex and g(x) = ln 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. log9(9x)
Write in exponential form: log5 125 = 3.
Fill in each blank so that the resulting statement is true.If e0.6x = 6, then 0.6x =_______ .
Fill in each blank so that the resulting statement is true.The change-of-base property for logarithms allows us to write logarithms with base b in terms of a new base a. Introducing base a, the property states that logb M =_______ . ________ .
Fill in each blank so that the resulting statement is true.For each of the scatter plots in Exercises 4–6, determine whether an exponential function, a logarithmic function, or a linear function is the best choice for modeling the data.__________ . y Х
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