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mathematics
precalculus 1st

Precalculus 1st Edition Jay Abramson - Solutions

For the following exercises, match each function with one of the graphs in Figure 12.f(x) = 4(0.69)x B C Figure 12 E
For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs.logb (7x · 2y)
Consider the general logarithmic function f(x) = logb (x). Why can’t x be zero?
For the following exercises, use the graphs shown in Figure 13. All have the form f(x) = abx .Which graph has the largest value for b? BACA Figure 13 D E X
For the following exercises, use logarithms to solve.−6e9x + 8 + 2 = −74
For the following exercises, rewrite each equation in logarithmic form.19x = y
For the following exercises, find the formula for an exponential function that passes through the two points given.(0, 2000) and (2, 20)
For the following exercises, condense each expression to a single logarithm using the properties of logarithms.log(2x4) + log(3x5)
For the following exercises, state the domain, vertical asymptote, and end behavior of the function.f(x) = log3 (15 − 5x) + 6
For the following exercises, use logarithms to solve.2x + 1 = 52x − 1
For the following exercises, use the graphs shown in Figure 13. All have the form f(x) = abx .Which graph has the smallest value for b? B+ CM Figure 13 D E Х
For the following exercises, find the formula for an exponential function that passes through the two points given. 23/1) and (3, 24) -1,
For the following exercises, rewrite each equation in logarithmic form.x−10/13 = y
For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote. x² f(x) = x² + 2x + 1
For the following exercises, use the written statements to construct a polynomial function that represents the required information.An open box is to be constructed by cutting out square corners of x-inch sides from a piece of cardboard 8 inches by 8 inches and then folding up the sides. Express
For the following exercises, construct a polynomial function of least degree possible using the given information.Real roots: −1/2 , 0, 1/2 and (−2, f(−2)) = (−2, 6)
For the following exercises, use a calculator to approximate local minima and maxima or the global minimum and maximum.f(x) = −x4 + 3x − 2
For the following exercises, use the given volume of a box and its length and width to express the height of the box algebraically. Volume is 10x3 + 30x2 − 8x − 24, length is 2, width is x + 3.
For the following exercises, use a calculator to find the answer.Graph on the same set of axes the functions f(x) = x2 , f(x) = 2x2 , and f(x) = 1/3 x2 . What appears to be the effect of changing the coefficient?
For the following exercises, use a calculator to graph f(x). Use the graph to solve f(x) > 0. f(x)= = 2 x+1
For the following exercises, use the written statements to construct a polynomial function that represents the required information.A rectangle is twice as long as it is wide. Squares of side 2 feet are cut out from each corner. Then the sides are folded up to make an open box. Express the volume
For the following exercises, construct a polynomial function of least degree possible using the given information.Real roots: −4, −1, 1, 4 and (−2, f(−2)) = (−2, 10)
For the following exercises, use a calculator to graph f(x). Use the graph to solve f(x) > 0. f(x) = 4 2x - 3
For the following exercises, use a calculator to approximate local minima and maxima or the global minimum and maximum.f(x) = x4 − x3 + 1
For the following exercises, use the given volume and radius of a cylinder to express the height of the cylinder algebraically.Volume is π(25x3 − 65x2 − 29x − 3), radius is 5x + 1.
For the following exercises, use a calculator to find the answer.Graph on the same set of axes f(x) = x2 , f(x) = x2 + 2 and f(x) = x2 , f(x) = x2 + 5 and f(x) = x2 − 3. What appears to be the effect of adding a constant?
For the following exercises, find the dimensions of the box described.The length is twice as long as the width. The height is 2 inches greater than the width. The volume is 192 cubic inches.
For the following exercises, use the graphs to write a polynomial function of least degree. f(x) (0,8) (9) -X
For the following exercises, use a calculator to graph f(x). Use the graph to solve f(x) > 0. f(x) = = 2 (x - 1)(x + 2)
For the following exercises, use the given volume and radius of a cylinder to express the height of the cylinder algebraically.Volume is π(4x3 + 12x2 − 15x − 50), radius is 2x + 5.
For the following exercises, use a calculator to find the answer. Graph on the same set of axes f(x) = x2 , f(x) = (x − 2)2 , f(x − 3)2 , and f(x) = (x + 4)2 . What appears to be the effect of adding or subtracting those numbers?
For the following exercises, use the graphs to write a polynomial function of least degree. 300 f(x) 610 (0, 50,000,000) 5-10 10. 3-10²4 210 1-10 100 -1-10 100 200 -210² -3-10- -410² -$-10 -6-10 -7-10 300 400 500 600 +++X 700
For the following exercises, find the dimensions of the box described.The length, width, and height are consecutive whole numbers. The volume is 120 cubic inches.
For the following exercises, use the given volume and radius of a cylinder to express the height of the cylinder algebraically.Volume is π(3x4 + 24x3 + 46x2 − 16x − 32), radius is x + 4.
For the following exercises, use a calculator to graph f(x). Use the graph to solve f(x) > 0. f(x)= x+2 (x - 1)(x-4)
For the following exercises, use a calculator to find the answer.The path of an object projected at a 45 degree angle with initial velocity of 80 feet per second is given by the function h(x) = −32/(80)2 x2 + x where x is the horizontal distance traveled and h(x) is the height in feet. Use the
For the following exercises, use the graphs to write a polynomial function of least degree. (-300,0) f(x) 2-10² 1-10 (100, 0) 30-200 -100 100 200 -1-10²(0, -90,000) -2.16 10 -4.10
For the following exercises, find the dimensions of the box described.The length is one inch more than the width, which is one inch more than the height. The volume is 86.625 cubic inches.
For the following exercises, use a calculator to find the answer. A suspension bridge can be modeled by the quadratic function h(x) = 0.0001x2 with −2000 ≤ x ≤ 2000 where ∣x∣ is the number of feet from the center and h(x) is height in feet. Use the [TRACE] feature of your calculator
For the following exercises, use a calculator to graph f(x). Use the graph to solve f(x) > 0. f(x) (x + 3)² (x - 1)²(x + 1)
For the following exercises, find the dimensions of the box described.The length is three times the height and the height is one inch less than the width. The volume is 108 cubic inches.
For the following exercises, write the polynomial function that models the given situation.A rectangle has a length of 10 units and a width of 8 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a
For the following exercises, identify the removable discontinuity. f(x) = x³ + 1 x+1
For the following exercises, use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function.Vertex (1, −2), opens up.
For the following exercises, find the dimensions of the box described.The length is 3 inches more than the width. The width is 2 inches more than the height. The volume is 120 cubic inches.
For the following exercises, write the polynomial function that models the given situation.Consider the same rectangle of the preceding problem. Squares of 2x by 2x units are cut out of each corner. Express the volume of the box as a polynomial in terms of x.
For the following exercises, use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function.Vertex (−1, 2) opens down.
For the following exercises, identify the removable discontinuity. f(x)= x²+x-6 x-2
For the following exercises, find the dimensions of the right circular cylinder described.The radius is 3 inches more than the height. The volume is 16π cubic meters.
For the following exercises, write the polynomial function that models the given situation.A square has sides of 12 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a function in terms of x.
For the following exercises, use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function.Vertex (−5, 11), opens down.
For the following exercises, find the dimensions of the right circular cylinder described.The height is one less than one half the radius. The volume is 72π cubic meters.
For the following exercises, identify the removable discontinuity. f(x) = 2x² + 5x 3 - x + 3
For the following exercises, write the polynomial function that models the given situation.A cylinder has a radius of x + 2 units and a height of 3 units greater. Express the volume of the cylinder as a polynomial function.
For the following exercises, use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function.Vertex (−100, 100), opens up.
For the following exercises, find the dimensions of the right circular cylinder described.The radius and height differ by one meter. The radius is larger and the volume is 48π cubic meters.
For the following exercises, identify the removable discontinuity. f(x)= x³ + x² x+1
For the following exercises, write the polynomial function that models the given situation.A right circular cone has a radius of 3x + 6 and a height 3 units less. Express the volume of the cone as a polynomial function. The volume of a cone is V = 1/3 πr2 h for radius r and height h.
For the following exercises, write the equation of the quadratic function that contains the given point and has the same shape as the given function.Contains (1, 1) and has shape of f(x) = 2x2 . Vertex is on the y-axis.
For the following exercises, find the dimensions of the right circular cylinder described.The radius and height differ by two meters. The height is greater and the volume is 28.125π cubic meters.
For the following exercises, write the equation of the quadratic function that contains the given point and has the same shape as the given function.Contains (−1, 4) and has the shape of f(x) = 2x2 . Vertex is on the y-axis.
For the following exercises, express a rational function that describes the situation.A large mixing tank currently contains 200 gallons of water, into which 10 pounds of sugar have been mixed. A tap will open, pouring 10 gallons of water per minute into the tank at the same time sugar is poured
For the following exercises, find the dimensions of the right circular cylinder described.The radius is 1/3 meter greater than the height. The volume is 98/9ππ cubic meters.
For the following exercises, write the equation of the quadratic function that contains the given point and has the same shape as the given function.Contains (2, 3) and has the shape of f(x) = 3x2 . Vertex is on the y-axis.
For the following exercises, express a rational function that describes the situation.A large mixing tank currently contains 300 gallons of water, into which 8 pounds of sugar have been mixed. A tap will open, pouring 20 gallons of water per minute into the tank at the same time sugar is poured
For the following exercises, write the equation of the quadratic function that contains the given point and has the same shape as the given function.Contains (1, −3) and has the shape of f(x) = −x2 . Vertex is on the y-axis.
For the following exercises, use the given rational function to answer the question. The concentration C of a drug in a patient’s bloodstream t hours after injection in given by C(t) =2t/3 + t2. What happens to the concentration of the drug as t increases?
For the following exercises, write the equation of the quadratic function that contains the given point and has the same shape as the given function. Contains (4, 3) and has the shape of f(x) = 5x2 . Vertex is on the y-axis.
For the following exercises, use the given rational function to answer the question. The concentration C of a drug in a patient’s bloodstream t hours after injection is given by C(t) = 100t/2t2 + 75. Use a calculator to approximate the time when the concentration is highest.
For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator to answer the question.An open box with a square base is to have a volume of 108 cubic inches. Find the dimensions of the box that will have minimum surface area. Let x = length of
Find the dimensions of the rectangular corral producing the greatest enclosed area given 200 feet of fencing.
For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator to answer the question.A rectangular box with a square base is to have a volume of 20 cubic feet. The material for the base costs 30 cents/square foot. The material for the sides
Find the dimensions of the rectangular corral split into 2 pens of the same size producing the greatest possible enclosed area given 300 feet of fencing.
For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator to answer the question.A right circular cylinder has volume of 100 cubic inches. Find the radius and height that will yield minimum surface area. Let x = radius.
Find the dimensions of the rectangular corral producing the greatest enclosed area split into 3 pens of the same size given 500 feet of fencing.
For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator to answer the question.A right circular cylinder with no top has a volume of 50 cubic meters. Find the radius that will yield minimum surface area. Let x = radius.
Among all of the pairs of numbers whose sum is 6, find the pair with the largest product. What is the product?
For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator to answer the question.A right circular cylinder is to have a volume of 40 cubic inches. It costs 4 cents/square inch to construct the top and bottom and 1 cent/square inch to
Among all of the pairs of numbers whose difference is 12, find the pair with the smallest product. What is the product?
Suppose that the price per unit in dollars of a cell phone production is modeled by p = $45 − 0.0125x, where x is in thousands of phones produced, and the revenue represented by thousands of dollars is R = x ⋅ p. Find the production level that will maximize revenue.
A rocket is launched in the air. Its height, in meters above sea level, as a function of time, in seconds, is given by h(t) = −4.9t2 + 229t + 234. Find the maximum height the rocket attains.
A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by h(t) = −4.9t2 + 24t + 8. How long does it take to reach maximum height?
A soccer stadium holds 62,000 spectators. With a ticket price of $11, the average attendance has been 26,000. When the price dropped to $9, the average attendance rose to 31,000. Assuming that attendance is linearly related to ticket price, what ticket price would maximize revenue?
A farmer finds that if she plants 75 trees per acre, each tree will yield 20 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest?
The inverse of every logarithmic function is an exponential function and vice-versa. What does this tell us about the relationship between the coordinates of the points on the graphs of each?
What role does the horizontal asymptote of an exponential function play in telling us about the end behavior of the graph?
How can an exponential equation be solved?
What is a base b logarithm? Discuss the meaning by interpreting each part of the equivalent equations by = x and logb (x) = y for b > 0, b ≠ 1.
Explain why the values of an increasing exponential function will eventually overtake the values of an increasing linear function.
How does the power rule for logarithms help when solving logarithms with the form logb (n√x)?
What type(s) of translation(s), if any, affect the range of a logarithmic function?
What is the advantage of knowing how to recognize transformations of the graph of a parent function algebraically?
When does an extraneous solution occur? How can an extraneous solution be recognized?
How is the logarithmic function f(x) = logb (x) related to the exponential function g(x) = bx ? What is the result of composing these two functions?
Given a formula for an exponential function, is it possible to determine whether the function grows or decays exponentially just by looking at the formula? Explain.
What does the change-of-base formula do? Why is it useful when using a calculator?
What type(s) of translation(s), if any, affect the domain of a logarithmic function?
The graph of f(x) = 3x is reflected about the y-axis and stretched vertically by a factor of 4. What is the equation of the new function, g(x)? State its y-intercept, domain, and range.
When can the one-to-one property of logarithms be used to solve an equation? When can it not be used?
How can the logarithmic equation logb x = y be solved for x using the properties of exponents?

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