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College Algebra 7th Edition Robert F Blitzer - Solutions

In Exercises 9–14, graph each equation in a rectangular coordinate system. If two functions are indicated, graph both in the same system.f(x) = ln x and g(x) = ln(x - 2) + 1
In Exercises 9–14, graph each equation in a rectangular coordinate system. If two functions are indicated, graph both in the same system. f(x) = x²1 2 x² - 4
In Exercises 11–18, solve each equation.e2x - 6ex + 5 = 0
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. 64 log4 y
In Exercises 11–18, solve each equation.400e0.005x = 1600
In Exercises 9–14, graph each equation in a rectangular coordinate system. If two functions are indicated, graph both in the same system.f(x) = 2x - 4 and f -1(x)
Fill in each blank so that the resulting statement is true.The logarithmic function with base 10 is called the________ logarithmic function. The function f(x) = log10 x is usually expressed as f(x) =________ .
In Exercises 9–14, graph each equation in a rectangular coordinate system. If two functions are indicated, graph both in the same system.f(x) = (x - 2)2(x + 1)
In Exercises 11–18, solve each equation.5x = 1.4
Use the compound interest formulas to solve Exercises 10–11.Suppose that you have $14,000 to invest. Which investment yields the greater return over 10 years: 7% compounded monthly or 6.85% compounded continuously?
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents.9x = 27
In Exercises 11–18, solve each equation.3x-2 = 9x+4
Fill in each blank so that the resulting statement is true.The graph of g(x) = -log4 x is the graph of f(x) = log4 x reflected about the_______ .
Use a calculator to evaluate log15 71 to four decimal places.
Fill in each blank so that the resulting statement is true.True or false: -10 is a solution of log5(x + 35) = 2.________
In Exercises 10–20, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log28+ log5 25
In Exercises 9–20, write each equation in its equivalent logarithmic form. 54 = 625
Use the compound interest formulas to solve Exercises 10–11.Suppose that you have $5000 to invest. Which investment yields the greater return over 5 years: 5.5% compounded semiannually or 5.25% compounded monthly?
In Exercises 9–14, complete the table. Round projected populations to one decimal place and values of k to four decimal places. Country Pakistan 2010 Population (millions) 184.4 Projected 2050 Projected Growth Rate, k 0.0149 Population (millions)
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 1000
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places.e-0.75
In Exercises 9–14, graph each equation in a rectangular coordinate system. If two functions are indicated, graph both in the same system.f(x) = (x - 2)2 - 1
Fill in each blank so that the resulting statement is true.The graph of g(x) = log3(x + 5) is the graph of f(x) = log3 x shifted_______ .
Fill in each blank so that the resulting statement is true.True or false: -3 is a solution of log5 9 = 2 log5 x.________
In Exercises 8–9, write each expression as a single logarithm.ln 7 - 3 ln x
In Exercises 6–9, find the domain of each function.f(x) = 3x+6
In Exercises 9–20, write each equation in its equivalent logarithmic form. 2³ = 8
The functions in Exercises 93–95 are all one-to-one. For each function,a. Find an equation for f -1(x), the inverse function.b. Verify that your equation is correct by showing that f(f -1(x)) = x and f -1(f(x)) = x. f(x) = x - 7 x + 2
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 minutes.• Additional time costs $0.30 per minute.Plan B• $40 per month buys 200 minutes.• Additional
Explain how to derive the slope-intercept form of a line’s equation, y = mx + b, from the point-slope form y - y1 = m(x - x1).
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 - 3
In Exercises 123–126, write a possible equation for the function whose graph is shown. Each graph shows a transformation of a common function. [-3, 3, 1] by [-6, 6, 1]
In Exercises 123–126, write a possible equation for the function whose graph is shown. Each graph shows a transformation of a common function. [-2, 8, 1] by [-1, 4, 1]
In Exercises 123–126, write a possible equation for the function whose graph is shown. Each graph shows a transformation of a common function. [-5, 3, 1] by [-5, 10, 1]
In Exercises 123–126, write a possible equation for the function whose graph is shown. Each graph shows a transformation of a common function. [-1, 9, 1] by [-1, 5, 1]
Fill in each blank so that the resulting statement is true.Consider the polynomial function with integer coefficientsThe Rational Zero Theorem states that if p/q is a rational zero of f (where p/q is reduced to lowest terms), then p is a factor of_____ and q is a factor of_______ . f(x) anx
Fill in each blank so that the resulting statement is true.All rational functions can be expressed aswhere p and q are_______ functions and q(x) ≠ 0. f(x) = p(x) q(x)'
In Exercises 1–4, the graph of a quadratic function is given. Write the function’s equation, selecting from the following options. f(x) = (x + 1)² - 1 h(x) = (x - 1)² + 1 g(x) = (x + 1)² + 1 j(x) = (x - 1)² - 1
Fill in each blank so that the resulting statement is true.We solve the polynomial inequality x2 + 8x + 15 > 0 by first solving the equation________ . The real solutions of this equation, -5 and -3, shown on the number line, are called_____ points. ? دل -7 -6 -5 -4 -3 -2 -2 -1 -1 0 1 2 + 3 X
In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x) = x³ + x² - 4x - 4
In Exercises 1–8, find the domain of each rational function. f(x) 5x x - 4
In Exercises 1–16, divide using long division. State the quotient, q(x), and the remainder, r(x). (x² + 8x + 15) + (x + 5)
In Exercises 1–4, graph the given quadratic function. Give each function’s domain and range.f(x) = (x - 3)2 - 4
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. (x4) (x + 2) >0
In Exercises 1–2, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola’s axis of symmetry. Use the graph to determine the function’s domain and range.f(x) = (x + 1)2 + 4
In Exercises 1–4, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola’s axis of symmetry. Use the graph to determine the function’s domain and range.f(x) = -(x + 1)2 + 4
Use the graph of y = f(x) to solve Exercises 1–6.Find the domain and the range of f. PRO y y = f(x) et X
In Exercises 1–4, the graph of a quadratic function is given. Write the function’s equation, selecting from the following options. f(x) = (x + 1)² - 1 h(x) = (x - 1)² + 1 g(x) = (x + 1)² + 1 j(x) = (x - 1)² - 1
Fill in each blank so that the resulting statement is true.Consider the following long division problem:We begin the division process by rewriting the dividend as________ . x + 4)6x4 + 2x³.
Fill in each blank so that the resulting statement is true.Consider the following long division problem:We begin the division process by dividing______ by______ . We obtain_______ . We write this result above_______ in the dividend. 3x - 1)6x³ + 7x² + 12x - 5.
Use the four-step procedure for solving variation problems given on page 445 to solve Exercises 1–10.y varies directly as x. y = 65 when x = 5. Find y when x = 12.
In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree.f(x) = 5x2 + 6x3
In Exercises 1–8, find the domain of each rational function. f(x) = 7x x-8
Fill in each blank so that the resulting statement is true.The degree of the polynomial function f(x) = -2x3(x - 1)(x + 5) is_______ . The leading coefficient is______ .
In Exercises 1–16, divide using long division. State the quotient, q(x), and the remainder, r(x). (x² + 3x - 10) 10) = (x - 2)
In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x) = x³ + 3x² - 6x - 8
Fill in each blank so that the resulting statement is true.y varies directly as x can be modeled by the equation_________ , where k is called the_______ .
In Exercises 1–2, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola’s axis of symmetry. Use the graph to determine the function’s domain and range.f(x) = x2 - 2x - 3
In Exercises 1–4, graph the given quadratic function. Give each function’s domain and range.f(x) = 5 - (x + 2)2
Fill in each blank so that the resulting statement is true.The quadratic function f(x) = a(x - h)2 + k, a ≠ 0, is in_________ form. The graph of f is called a/an________ whose vertex is the point_______ . The graph opens upward if a________ and opens downward if a______ .
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. (x+3)(x - 5) > 0
In Exercises 1–4, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola’s axis of symmetry. Use the graph to determine the function’s domain and range.f(x) = (x + 4)2 - 2
Fill in each blank so that the resulting statement is true.True or false: 3/2 is a possible rational zero of f(x) = 2x3 + 11x2 - 7x - 6.______
Fill in each blank so that the resulting statement is true.The points at -5 and -3 shown in Exercise 1 divide the number line into three intervals:________,____________ ,____________ .
Fill in each blank so that the resulting statement is true.True or false: Some polynomial functions of degree 2 or higher have breaks in their graphs________.
Use the graph of y = f(x) to solve Exercises 1–6.Find the zeros and the least possible multiplicity of each zero. PRO y y = f(x) et X
Use the four-step procedure for solving variation problems given on page 445 to solve Exercises 1–10.y varies directly as x. y = 45 when x = 5. Find y when x = 13.
Fill in each blank so that the resulting statement is true.y varies directly as the nth power of x can be modeled by the equation________.
Fill in each blank so that the resulting statement is true.In the following long division problem, the first step has been completed:The next step is to multiply______ and_______ . We obtain______ . We write this result below______ . 2x² 5x 210x³ + 6x² - 9x + 10.
In Exercises 1–4, graph the given quadratic function. Give each function’s domain and range.f(x) = -x2 - 4x + 5
Fill in each blank so that the resulting statement is true.In the following long division problem, most of the steps have been completed:Completing the step designated by the question mark, we obtain______ . Thus, the quotient is_______ and the remainder is_______ . The answer to this long division
Fill in each blank so that the resulting statement is true.Consider the rational inequality Setting the numerator and the denominator of equal to zero, we obtain x = 1 and x = -2. These values are shown as points on the number line. Also shown is information about three test values.Based on the
In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. h(x) = 7x³ + 2x² + 1 X
In Exercises 1–8, find the domain of each rational function. h(x) = x + 7 x² - 49
In Exercises 5–6, use the function’s equation, and not its graph, to finda. The minimum or maximum value and where it occurs.b. The function’s domain and its range.f(x) = -x2 + 14x - 106
Among all pairs of numbers whose sum is 14, find a pair whose product is as large as possible. What is the maximum product?
Fill in each blank so that the resulting statement is true.If the graph of a function f approaches b as x increases or decreases without bound, then the line y = b is a/an of the graph of f. The equation of such a line for the graph of y = x - 10/3x2 + x + 1 is_________ . The equation of such a
In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x) = 3x4 11x³ - 3x² - 6x + 8 -
In Exercises 1–4, the graph of a quadratic function is given. Write the function’s equation, selecting from the following options. P -4-3-2- y 4- IIIP²HI [D X
In Exercises 1–8, find the domain of each rational function. g(x) 3x² (x - 5)(x + 4)
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. (x-7)(x + 3) ≤ 0
In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. g(x) = 7x5 – πχ + 1 5
In Exercises 1–16, divide using long division. State the quotient, q(x), and the remainder, r(x). (x³ + 5x² + 7x + 2) = (x + 2)
In Exercises 1–4, the graph of a quadratic function is given. Write the function’s equation, selecting from the following options. f(x) = (x + 1)² - 1 h(x) = (x - 1)² + 1 g(x) = (x + 1)² + 1 j(x) = (x - 1)² - 1
In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x) = 3x4 - 11x³− x² + 19x + 6
In Exercises 1–4, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola’s axis of symmetry. Use the graph to determine the function’s domain and range.f(x) = -x2 + 2x + 3
Fill in each blank so that the resulting statement is true.True or false: 1/2 is a possible rational zero of f(x) = 3x4 - 3x3 + x2 - x + 1.______
Use the graph of y = f(x) to solve Exercises 1–6.Where does the relative maximum occur? PRO y y = f(x) et X
Fill in each blank so that the resulting statement is true.True or false: The graph of the reciprocal function f(x) = 1/x has a break and is composed of two distinct branches._________
In Exercises 1–8, find the domain of each rational function. g(x) = 2x² (x − 2)(x + 6)
In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x) = 2x² + 3x³ - 11x²9x + 15
In Exercises 1–16, divide using long division. State the quotient, q(x), and the remainder, r(x). 2x²5x + 6) + (x − 3) (x³ - 2x²
Fill in each blank so that the resulting statement is true.True or false: A test value for the leftmost interval on the number line shown in Exercise 1 could be -10._______
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. (x + 1)(x-7) ≤ 0.
In Exercises 1–4, graph the given quadratic function. Give each function’s domain and range.f(x) = 3x2 - 6x + 1
Use the graph of y = f(x) to solve Exercises 1–6.Find (f ° f )(-1). PRO y y = f(x) et X
Fill in each blank so that the resulting statement is true.In the following long division problem, the first two steps have been completed:The next step is to subtract_______ from_______ . We obtain_______ . Then we bring down______ and form the new dividend________. 2x 3x - 5)6x2 + 8x - 4. 6x2 -
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. rẻ – 5r+4>0
Use the four-step procedure for solving variation problems given on page 445 to solve Exercises 1–10.y varies inversely as x. y = 12 when x = 5. Find y when x = 2.
Use the graph of y = f(x) to solve Exercises 1–6.Use arrow notation to complete this statement: f(x) → ∞ as _____ or as _____. PRO y y = f(x) et X

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