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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

The table lists numbers of titles T released for DVD rentals x years after 1995.(a) Find a power function f that models the data in the table. (b) Use to estimate the number of titles released in
If an object is dropped from a height h, then the time t required for the object to strike the ground is directly proportional to the square root of h. If it requires 1 second for an object to fall
The table lists numbers N of Walmart employees (in millions) x years after 1980.(a) Find a power function of that models the data in the table.(b) Use f to predict the number of employees in the year
The wingspan L in feet of a bird weighing W pounds is given by L = 2.43W0.3326 Estimate the wingspan of a bird that weighs 5.2 pounds.
Suppose that the surface area S of a bird's wings in square feet can be modeled by S(w) = 1.27w2/3, where w is the weight of the bird in pounds, with 1 ≤ w ≤ 10. Estimate the weight of a bird
The table contains data that can be modeled by a function of the form f(x) = axb. Use regres- sion to find the constants a and b to the nearest hundredth. Graph fand the data.
The table contains data that can be modeled by a function of the form f(x) = axb. Use regres- sion to find the constants a and b to the nearest hundredth. Graph fand the data.
Graph y = n√x for n = 2, 4, generalizations about a graph of and 6. State some an even root function.
Graph y = n√x for n = 3, 5, about a graph of and 7. State some generalizations an odd root function.
One study showed that for a male fiddler crab weighing over 0.75 gram, the weight of its claws can be estimated by f(x) = 0.445x5/4 The input x is the weight of the crab in grams, and the output f(x)
The formula f(x) = x1.5 calculates the number of years it takes for a planet to orbit the sun if its average distance from the sun is x times that of Earth. If there were a planet located 15 times as
The average weight in pounds for men and women can sometimes be estimated by f(x) = ax1.7, where x is a person's height in inches and a is a constant determined by the sex of the individual. (a)
Use the results in the previous exercise to calculate the pulse rates for a 60-pound dog and a 2-ton whale.
Explain the basic steps needed to solve equations that contain square roots of variables.
Can a function be both a polynomial function and a power function? Explain.
In Exercises 57–80, follow the seven steps to graph each rational function.Seven Steps are given below Strategy for Graphing a Rational Function The following strategy can be used to
Use Descartes’s Rule of Signs to determine the possible number of positive and negative real zeros of f(x) = x5 - x4 + x3 - x2 + x - 8. Verify your result by using a graphing utility to graph f.
What are the zeros of a polynomial function and how are they found?
In Exercises 65–72, complete graphs of polynomial functions whose zeros are integers are shown.a. Find the zeros and state whether the multiplicity of each zero is even or odd.b. Write an equation,
In Exercises 57–80, follow the seven steps to graph each rational function.Seven Steps are given below Strategy for Graphing a Rational Function The following strategy can be used to
Solve each inequality in Exercises 65–70 and graph the solution set on a real number line. x²-3x + 2 X² 2x - 3 > 0
In Exercises 71–72, use the graph of the polynomial function to solve each inequality. f(x) = 2x³ + 11x² – 7x − 6 [-7, 3, 1] by [-10, 70, 10]
In Exercises 57–80, follow the seven steps to graph each rational function.Seven Steps are given below Strategy for Graphing a Rational Function The following strategy can be used to
In Exercises 65–72, complete graphs of polynomial functions whose zeros are integers are shown.a. Find the zeros and state whether the multiplicity of each zero is even or odd.b. Write an equation,
In Exercises 57–80, follow the seven steps to graph each rational function.Seven Steps are given below Strategy for Graphing a Rational Function The following strategy can be used to
A rain gutter is made from sheets of aluminum that are 20 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross- sectional area and
In Exercises 65–72, complete graphs of polynomial functions whose zeros are integers are shown.a. Find the zeros and state whether the multiplicity of each zero is even or odd.b. Write an equation,
In Exercises 57–80, follow the seven steps to graph each rational function.Seven Steps are given below Strategy for Graphing a Rational Function The following strategy can be used to
In Exercises 71–72, use the graph of the polynomial function to solve each inequality. f(x) = 2x³ + 11x² – 7x − 6 [-7, 3, 1] by [-10, 70, 10]
In Exercises 73–74, use the graph of the rational function to solve each inequality. f(x) = x + 1 1²-4 [-4, 4, 1] by [-4, 4, 1]
Experts fear that without conservation efforts, tigers could disappear from the wild by 2022. Just one hundred years ago, there were at least 100,000 wild tigers. By 2010, the estimated world tiger
In Exercises 57–80, follow the seven steps to graph each rational function.Seven Steps are given below Strategy for Graphing a Rational Function The following strategy can be used to
In Exercises 57–80, follow the seven steps to graph each rational function.Seven Steps are given below Strategy for Graphing a Rational Function The following strategy can be used to
Suppose 3/4 is a root of a polynomial equation. What does this tell us about the leading coefficient and the constant term in the equation?
In Exercises 73–74, use the graph of the rational function to solve each inequality. f(x) = x + 1 1²-4 [-4, 4, 1] by [-4, 4, 1]
The equations in Exercises 72–75 have real roots that are rational. Use the Rational Zero Theorem to list all possible rational roots. Then graph the polynomial function in the given viewing
In Exercises 70–73, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.Synthetic division can be used to find the
Experts fear that without conservation efforts, tigers could disappear from the wild by 2022. Just one hundred years ago, there were at least 100,000 wild tigers. By 2010, the estimated world tiger
A rain gutter is made from sheets of aluminum that are 12 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and
Hunky Beef, a local sandwich store, has a fixed weekly cost of $525.00, and variable costs for making a roast beef sandwich are $0.55.a. Let x represent the number of roast beef sandwiches made and
In Exercises 70–73, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.Any problem that can be done by synthetic
The equations in Exercises 72–75 have real roots that are rational. Use the Rational Zero Theorem to list all possible rational roots. Then graph the polynomial function in the given viewing
The equations in Exercises 72–75 have real roots that are rational. Use the Rational Zero Theorem to list all possible rational roots. Then graph the polynomial function in the given viewing
In Exercises 70–73, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.If a polynomial long-division problem
Find k so that 4x + 3 is a factor of 20x3 + 23x2 - 10x + k.
The equations in Exercises 72–75 have real roots that are rational. Use the Rational Zero Theorem to list all possible rational roots. Then graph the polynomial function in the given viewing
When 2x2 - 7x + 9 is divided by a polynomial, the quotient is 2x - 3 and the remainder is 3. Find the polynomial.
During a diagnostic evaluation, a 33-year-old woman experienced a panic attack a few minutes after she had been asked to relax her whole body. The graph shows the rapid increase in heart rate during
Notice that the figure does not specify which graph is the model for dry roads and which is the model for wet roads. Use this information to solve Exercises 77–78.a. Use the given functions at the
In Exercises 57–80, follow the seven steps to graph each rational function.Seven Steps are given below Strategy for Graphing a Rational Function The following strategy can be used to
Use the position functionto answer Exercises 75–76.You throw a ball straight up from a rooftop 160 feet high with an initial velocity of 48 feet per second. During which time period will the
Notice that the figure does not specify which graph is the model for dry roads and which is the model for wet roads. Use this information to solve Exercises 77–78.a. Use the given functions at the
Volatility at the Pump The graph shows the average price per gallon of gasoline in the United States in January for the period from 2005 through 2011.a. For which years was the average price per
In Exercises 57–80, follow the seven steps to graph each rational function.Seven Steps are given below Strategy for Graphing a Rational Function The following strategy can be used to
In Exercises 57–80, follow the seven steps to graph each rational function.Seven Steps are given below Strategy for Graphing a Rational Function The following strategy can be used to
Use Descartes’s Rule of Signs to determine the possible number of positive and negative real zeros of f(x) = 3x4 + 5x2 + 2. What does this mean in terms of the graph of f? Verify your result by
Find the quotient of x3n + 1 and xn + 1.
What is a parabola? Describe its shape.
In Exercises 57–80, follow the seven steps to graph each rational function.Seven Steps are given below Strategy for Graphing a Rational Function The following strategy can be used to
Use the graph of y = f(x) to graph y = 2f(x + 1) - 3. * * * دن دن y y = f(x) H -5-4-3-2-1. 1 2 3 4 5 X #
Given f(x) = 2x - 3 and g(x) = 2x2 - x + 5, find each of the following: a. (fog)(x) b. (gof)(x) C. (gof) (1).
In Exercises 81–88,a. Find the slant asymptote of the graph of each rational function.b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x) 2-1 X X
Explain how to decide whether a parabola opens upward or downward.
In Exercises 81–88,a. Find the slant asymptote of the graph of each rational function.b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x) 2-4 x² X
Synthetic division is a process for dividing a polynomial by x - c. The coefficient of x in the divisor is 1. How might synthetic division be used if you are dividing by 2x - 4?
The perimeter of a rectangle is 50 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 114 square feet.
Use synthetic division to show that 5 is a solution of x4 - 4x3 - 9x2 + 16x + 20 = 0. Then solve the polynomial equation.
What is a polynomial function?
Describe how to find a parabola’s vertex if its equation is expressed in standard form. Give an example.
Write equations for several polynomial functions of odd degree and graph each function. Is it possible for the graph to have no real zeros? Explain. Try doing the same thing for polynomial functions
What do we mean when we describe the graph of a polynomial function as smooth and continuous?
Use a graphing utility to obtain a complete graph for each polynomial function in Exercises 79–82. Then determine the number of real zeros and the number of imaginary zeros for each function.f(x) =
In Exercises 57–80, follow the seven steps to graph each rational function.Seven Steps are given below Strategy for Graphing a Rational Function The following strategy can be used to
Describe how to find a parabola’s vertex if its equation is in the form f(x) = ax2 + bx + c. Use f(x) = x2 - 6x + 8 as an example.
A parabola that opens upward has its vertex at (1, 2). Describe as much as you can about the parabola based on this information. Include in your discussion the number of x-intercepts (if any) for the
The perimeter of a rectangle is 180 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 800 square feet.
Use a graphing utility to obtain a complete graph for each polynomial function in Exercises 79–82. Then determine the number of real zeros and the number of imaginary zeros for each function.f(x) =
a. Use a graphing utility to graph y = 2x2 - 82x + 720 in a standard viewing rectangle. What do you observe?b. Find the coordinates of the vertex for the given quadratic function.c. The answer to
In Exercises 57–80, follow the seven steps to graph each rational function.Seven Steps are given below Strategy for Graphing a Rational Function The following strategy can be used to
What is meant by the end behavior of a polynomial function?
In Exercises 41–64,a. Use the Leading Coefficient Test to determine the graph’s end behavior.b. Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns
In Exercises 57–80, follow the seven steps to graph each rational function.Seven Steps are given below Strategy for Graphing a Rational Function The following strategy can be used to
Use a graphing utility to obtain a complete graph for each polynomial function in Exercises 79–82. Then determine the number of real zeros and the number of imaginary zeros for each function.f(x) =
In Exercises 41–64,a. Use the Leading Coefficient Test to determine the graph’s end behavior.b. Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns
Explain how to use the Leading Coefficient Test to determine the end behavior of a polynomial function.
In Exercises 82–85, find the vertex for each parabola. Then determine a reasonable viewing rectangle on your graphing utility and use it to graph the quadratic function.y = -0.25x2 + 40x
In Exercises 61–64, find the domain of each function. f(x) = = X V 2x 1 - 1
Use a graphing utility to obtain a complete graph for each polynomial function in Exercises 79–82. Then determine the number of real zeros and the number of imaginary zeros for each function.f(x) =
Exercises 82–84 will help you prepare for the material covered in the next section.Solve: x2 + 4x - 1 = 0.
Solve each inequality in Exercises 65–70 and graph the solution set on a real number line. x² + 2x - 36 > 12
Why is a third-degree polynomial function with a negative leading coefficient not appropriate for modeling nonnegative real-world phenomena over a long period of time?
Use the graph of the function modeling the volume of the carry-on luggage to solve Exercises 63–64.a. Identify your answers from Exercise 62 as points on the graph.b. Use the graph to describe a
In Exercises 82–85, find the vertex for each parabola. Then determine a reasonable viewing rectangle on your graphing utility and use it to graph the quadratic function.y = -4x2 + 20x + 160
You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area.
In Exercises 57–80, follow the seven steps to graph each rational function.Seven Steps are given below Strategy for Graphing a Rational Function The following strategy can be used to
In Exercises 65–72, complete graphs of polynomial functions whose zeros are integers are shown.a. Find the zeros and state whether the multiplicity of each zero is even or odd.b. Write an equation,
Solve each inequality in Exercises 65–70 and graph the solution set on a real number line. 8 < [L + x9 + zx
Among all pairs of numbers whose difference is 16, find a pair whose product is as small as possible. What is the minimum product?
In Exercises 83–86, determine whether each statement makes sense or does not make sense, and explain your reasoning.I’ve noticed that f(-x) is used to explore the number of negative real zeros of
How can the Factor Theorem be used to determine if x - 1 is a factor of x3 - 2x2 - 11x + 12?

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