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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

The loudness of a stereo speaker, measured in decibels, varies inversely as the square of your distance from the speaker. When you are 8 feet from the speaker, the loudness is 28 decibels. What is
The time required to assemble computers varies directly as the number of computers assembled and inversely as the number of workers. If 30 computers can be assembled by 6 workers in 10 hours, how
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) = x² + 4 X
In Exercises 83–86, determine whether each statement makes sense or does not make sense, and explain your reasoning.By using the quadratic formula, I do not need to bother with synthetic division
The bar graph shows the ratings of American Idol from season 1 (2002) through season 12 (2013).a. Let x represent American Idol’s season number and let y represent the average number of viewers, in
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) = x² = x +
Solve each inequality in Exercises 86–91 using a graphing utility. x² + 3x - 100
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) = x³
In Exercises 83–86, determine whether each statement makes sense or does not make sense, and explain your reasoning.I’m working with the polynomial function f(x) = x4 + 3x2 + 2 that has four
Solve each inequality in Exercises 86–91 using a graphing utility. 2x² + 5x - 30
Can the graph of a polynomial function have no x-intercepts? Explain.
In Exercises 87–90, determine whether each statement makes sense or does not make sense, and explain your reasoning.I must have made an error when graphing this parabola because its axis of
In Exercises 87–90, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The equation x3 + 5x2 + 6x + 1 = 0 has one
Can the graph of a polynomial function have no y-intercept? Explain.
In Exercises 87–90, determine whether each statement makes sense or does not make sense, and explain your reasoning.I like to think of a parabola’s vertex as the point where it intersects its
Heart rates and life spans of most mammals can be modeled using inverse variation. The bar graph shows the average heart rate and the average life span of five mammals.a. A mammal’s average life
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) = x² +
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) = x²+x-6 x
The volume of a pyramid varies jointly as its height and the area of its base. A pyramid with a height of 15 feet and a base with an area of 35 square feet has a volume of 175 cubic feet. Find the
Exercises 82–84 will help you prepare for the material covered in the next section.Solve: x2 + 4x + 6 = 0.
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 = 5x2 + 40x + 600
Exercises 82–84 will help you prepare for the material covered in the next section.Let f(x) = an (x4 - 3x2 - 4). If f(3) = -150, determine the value of an.
Explain the relationship between the multiplicity of a zero and whether or not the graph crosses or touches the x-axis and turns around at that zero.
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) = x³ -
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 = 0.01x2 + 0.6x + 100
If f is a polynomial function, and f(a) and f(b) have opposite signs, what must occur between a and b? If f(a) and f(b) have the same sign, does it necessarily mean that this will not occur? Explain
In Exercises 83–86, determine whether each statement makes sense or does not make sense, and explain your reasoning.I’m working with a fourth-degree polynomial function with integer coefficients
Explain the relationship between the degree of a polynomial function and the number of turning points on its graph.
Solve each inequality in Exercises 86–91 using a graphing utility. x³ + x² - 4x4>0 X
In Exercises 87–90, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.Descartes’s Rule of Signs gives the
In Exercises 87–90, determine whether each statement makes sense or does not make sense, and explain your reasoning.I threw a baseball vertically upward and its path was a parabola.
Solve each inequality in Exercises 86–91 using a graphing utility. x - 4 x-1 ≤0
In Exercises 89–94, the equation for f is given by the simplified expression that results after performing the indicated operation. Write the equation for f and then graph the function. 5x² x² +
In Exercises 87–90, determine whether each statement makes sense or does not make sense, and explain your reasoning.Figure 3.7 shows that a linear function provides a better description of the
Describe a strategy for graphing a polynomial function. In your description, mention intercepts, the polynomial’s degree, and turning points.
In Exercises 87–90, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.Every polynomial equation of degree 3 with
A popular model of carry-on luggage has a length that is 10 inches greater than its depth. Airline regulations require that the sum of the length, width, and depth cannot exceed 40 inches. These
Exercises 61–63 will help you prepare for the material covered in the first section of the next chapter.Use point plotting to graph f(x) = 2x. Begin by setting up a partial table of coordinates,
In Exercises 61–64, find the domain of each function. f(x) = √2x²5x + 2
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 ball is thrown upward and outward from a height of 6 feet. The height of the ball, f(x), in feet, can be modeled bywhere x is the ball’s horizontal distance, in feet, from where it was thrown.a.
Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. X x + 2 IV 2
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 57–64, find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant asymptote, if there is one, of the graph of each rational function. Then graph the
A popular model of carry-on luggage has a length that is 10 inches greater than its depth. Airline regulations require that the sum of the length, width, and depth cannot exceed 40 inches. These
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
State the Remainder Theorem. The Remainder Theorem If the polynomial f(x) is divided by x - c, then the remainder is f(c).
Find the inverse of f(x) = x3 + 2.
Among all pairs of numbers whose sum is 16, find a pair whose product is as large as possible. What is the maximum product?
In Exercises 61–64, find the domain of each function. f(x) = √4x² 1 9x + 2
In Exercises 57–64, find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant asymptote, if there is one, of the graph of each rational function. Then graph the
Among all pairs of numbers whose sum is 20, find a pair whose product is as large as possible. What is the maximum product?
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 61 as points on the graph.b. Use the graph to describe a
In Exercises 61–64, find the domain of each function. f(x) = 2x √x + 1 1
A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Four hundred feet of fencing is used. Find the dimensions of the playground
In Exercises 69–74, solve each inequality and graph the solution set on a real number line.2x2 + 9x + 4 ≥ 0
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 rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Six hundred feet of fencing is used. Find the dimensions of the playground
A company is planning to manufacture affordable graphing calculators. The fixed monthly cost will be $50,000 and it will cost $25 to produce each calculator.a. Write the cost function, C, of
In Exercises 69–74, solve each inequality and graph the solution set on a real number line.2x2 + 5x - 3 < 0
If you know that -2 is a zero of f(x) = x³ + 7x² + 4x - 12, explain how to solve the equation x³ + 7x² + 4x 12 = 0.
In Exercises 57–64, find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant asymptote, if there is one, of the graph of each rational function. Then graph the
Exercises 61–63 will help you prepare for the material covered in the first section of the next chapter.Use point plotting to graph f(x) = 2x. Begin by setting up a partial table of coordinates,
Describe how to find the possible rational zeros of a polynomial function.
The bar graph shows the population of the United States, in millions, for six selected years.a. Write a function that models the total U.S. population, P(x), in millions, x years after 1985.b. Write
Exercises 66–67 involve rational functions that model the given situations. In each case, find the horizontal asymptote as x → ∞ and then describe what this means in practical terms.the
In Exercises 66–69, determine whether each statement makes sense or does not make sense, and explain your reasoning.Every time I divide polynomials using synthetic division, I am using a highly
Exercises 66–67 involve rational functions that model the given situations. In each case, find the horizontal asymptote as x → ∞ and then describe what this means in practical terms.the number
Solve the equation. Check your answers. √x + 1 = √2x - 1
Complete the following. (a) Find the domain of f. (b) Graph f in an appropriate viewing rectangle. (c) Find any horizontal or vertical asymptotes. (d) Sketch a graph of f that includes any
Complete the following. (a) Find the domain of f. (b) Graph f in an appropriate viewing rectangle. (c) Find any horizontal or vertical asymptotes. (d) Sketch a graph of f that includes any
Solve the rational inequality (a) Symbolically and (b) Graphically. 4 x + 3 ≥0
Solve the rational inequality (a) Symbolically and (b) Graphically. x-1 x+1 0
Complete each of the following for f(x). (a) If possible, evaluate f(0) and f(-2). (b) Sketch a graph of f. Give the domain and range. (c) Over what interval(s) is the graph of y = f(x)
Complete each of the following for f(x). (a) If possible, evaluate f(0) and f(-2). (b) Sketch a graph of f. Give the domain and range. (c) Over what interval(s) is the graph of y = f(x)
Complete each of the following for f(x). (a) If possible, evaluate f(0) and f(-2). (b) Sketch a graph of f. Give the domain and range. (c) Over what interval(s) is the graph of y = f(x)
Give the domain of the power function. Approximate f(3) to the nearest hundredth. 2x¹/4+3=6
Solve the equation. Check your answers. * = S + ZA
Solve the rational inequality 1 (x - 1)² ≤0
Graph y = f(x). You may want to use division, factoring, or transformations as an aid. Show all asymptotes and "holes." f(x) = 2x²-3x - 2 x² - 4x + 4
Give the domain of the power function. Approximate f(3) to the nearest hundredth. 1³/2 = 27
Give the domain of the power function. Approximate f(3) to the nearest hundredth. 2n-² - 5n-¹
Evaluate each f(x) at the given x. Approximate each result to the nearest hundredth. f(x) = x-³/4 x-3/4, x = 7
Give the domain of the power function. Approximate f(3) to the nearest hundredth. m³ + 2m² + m²¹ = 0
Graph y = f(x). You may want to use division, factoring, or transformations as an aid. Show all asymptotes and "holes." f(x) = x²-x-2 x²-2x-3
Use translations to graph f. f(x) = (x - 1)¹/4
Match f(x) with its graph. Assume that a and b are constants with 0 f(x) = xª
Solve the rational inequality 2 (x + 1)² ≥0
The formulaapproximates the ocean temperature in degrees Fahrenheit at Naples, Florida. In this formula m is the month, with m = 1 corresponding to January. (a) What is the average ocean temperature
Use translations to graph f. f(x) = (x + 1)2/3 - 2
Taller animals tend to take longer, but fewer, steps per second than shorter animals. The relationship between the shoulder height / in meters of an animal and an animal's stepping frequency F in
Use translations to graph f. f(x) = (x - 1)²/3
Use the data in the table to complete the following.(a) Make a scatterplot of the data. Estimate a value for b so that f(x) = 0.0002xb models the data. (b) Check the accuracy of f(x). (c) The moon
Solve the equation. Check your answers. 6x-2/3-13x-1/3 - 5 = 0
Let the distance from home in miles of a person after t hours on a straight path be given by s(t). Approximate the average rate of change of s from t1 = 1/2 to t2 = 9/2 to the nearest tenth and
Find possible dimensions that minimize the surface area of a box with no top that has a volume of 96 cubic inches and a length that is three times the width.
Rainbow trout are sensitive to zinc ions in the water. High concentrations are lethal. The average survival times x in minutes for trout in various concentrations of zinc ions y in mil- ligrams per
Let the distance from home in miles of a person after t hours on a straight path be given by s(t). Approximate the average rate of change of s from t1 = 1/2 to t2 = 9/2 to the nearest tenth and
If there were a planet that took 200 years to orbit the sun, what would be its average distance x from the sun compared to that of Earth? Earth (Not to scale) Planet

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