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mathematics
precalculus

Questions and Answers of Precalculus

What is the domain of the function f(x) = √x – 2/x + 4?
In problem, construct a polynomial function that might have the given graph.
In problem, find bounds to the real zeros of each polynomial function.f(x) = 2x3 - 7x2 - 10x + 35
In problem, solve each equation in the real number system.x3 - 2/3x2 + 8/3x + 1 = 0
What is the domain of the function f(x) = √x3 - 3x2?
In problem, identify which of the graphs could be the graph of a polynomial function. For those that could, list the real zeros and state the least degree the polynomial can have. For those that
In problem, find bounds to the real zeros of each polynomial function.f(x) = x3 + x2 - 10x - 5
In problem, solve each equation in the real number system.x4 - 2x3 + 10x2 - 18x + 9 = 0
What is the domain of the function f(x) = √x4 - 16?
In problem, identify which of the graphs could be the graph of a polynomial function. For those that could, list the real zeros and state the least degree the polynomial can have. For those that
In problem, find bounds to the real zeros of each polynomial function.f(x) = x3 - x2 - 4x + 2
In problem, solve each equation in the real number system.x4 + 4x3 + 2x2 - x + 6 = 0
For what positive numbers will the cube of a number be less than the number?
Make up a rational function that has y = 2x + 1 as an oblique asymptote. Explain the methodology that you used.
In problem, identify which of the graphs could be the graph of a polynomial function. For those that could, list the real zeros and state the least degree the polynomial can have. For those that
In problem, solve each equation in the real number system.2x4 + 7x3 - 5x2 - 28x - 12 = 0
In problem, solve each equation in the real number system.2x3 - 11x2 + 10x + 8 = 0
For what positive numbers will the cube of a number exceed four times its square?
In problem, identify which of the graphs could be the graph of a polynomial function. For those that could, list the real zeros and state the least degree the polynomial can have. For those that
In problem, solve each equation in the real number system.2x4 + 7x3 + x2 - 7x - 3 = 0
Can the graph of a rational function have both a horizontal and an oblique asymptote? Explain.
Create a rational function that has the following characteristics: crosses the x-axis at 3; touches the x-axis at -2; one vertical asymptote, x = 1; and one horizontal asymptote, y = 2. Give your
In problem, solve each equation in the real number system.3x3 - x2 - 15x + 5 = 0
In problem, solve each equation in the real number system.3x4 + 3x3 - 17x2 + x - 6 = 0
In problem, solve each inequality algebraically.x3 – x ≥ 0
In problem, for each polynomial function:(a) List each real zero and its multiplicity.(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.(c) Determine the behavior of
If the graph of a rational function R has the horizontal asymptote y = 2, the degree of the numerator of R equals the degree of the denominator of R. Explain why.
Create a rational function that has the following characteristics: crosses the x-axis at 2; touches the x-axis at -1; one vertical asymptote at x = -5 and another at and one horizontal asymptote, y =
In problem, solve each equation in the real number system.2x3 - 3x2 - 3x - 5 = 0
In problem, solve each equation in the real number system.2x4 + 2x3 - 11x2 + x - 6 = 0
In problem, solve each inequality algebraically.x3 - 9x ≤ 0
In problem, for each polynomial function:(a) List each real zero and its multiplicity.(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.(c) Determine the behavior of
If the graph of a rational function R has the vertical asymptote x = 4, the factor x - 4 must be present in the denominator of R. Explain why.
In problem, solve each equation in the real number system.3x3 + 4x2 - 7x + 2 = 0
In problem, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers.f(x) = x4 + 6x3 + 11x2 + 12x + 18
In problem, solve each inequality algebraically.x + -12/x < 7
In problem, for each polynomial function:(a) List each real zero and its multiplicity.(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.(c) Determine the behavior of
Graph each of the following functions:What similarities do you see? What differences? x2 y = х6 х — 1 х8 y = х — 1 y = х — 1 y = х — 1
In problem, solve each equation in the real number system.2x3 + 3x2 + 2x + 3 = 0
In calculus you will learn that, ifis a polynomial function, then the derivative of P(x) isNewton's Method is an efficient method for approximating the x-intercepts (or real zeros) of a function,
In problem, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers.f(x) = x4 - 4x3 + 9x2 - 20x + 20
In problem, solve each inequality algebraically.6x - 5 < 6/x
In problem, for each polynomial function:(a) List each real zero and its multiplicity.(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.(c) Determine the behavior of
Graph each of the following functions:Is x = 1 a vertical asymptote? Why not? What is happening for x = 1? What do you conjecture about y = xn €“ 1/x €“ 1 x ‰¥ 1 an
In problem, solve each equation in the real number system.x4 - x3 + 2x2 - 4x - 8 = 0
From Ohm's law for circuits, it follows that the total resistance Rtot of two components hooked in parallel is given by the equationwhere R1 and R2 are the individual resistances.(a) Let R1 = 10
In problem, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers.f(x) = 4x3 - 4x2 - 7x - 2
In problem, solve each inequality algebraically.(x - 3)(x + 2) < x2 + 3x + 5
In problem, for each polynomial function:(a) List each real zero and its multiplicity.(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.(c) Determine the behavior of
A steel drum in the shape of a right circular cylinder is required to have a volume of 100 cubic feet.(a) Express the amount A of material required to make the drum as a function of the radius r of
A rare species of insect was discovered in the Amazon Rain Forest.To protect the species, environmentalists declared the insect endangered and transplanted the insect into a protected area. The
In problem, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers.f(x) = 3x4 + 4x3 + 7x2 + 8x + 2
In problem, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers.f(x) = 4x3 + 4x2 - 7x + 2
In problem, solve each inequality algebraically.3(x2 - 2) < 2(x - 1) 2 + x2
In problem, for each polynomial function:(a) List each real zero and its multiplicity.(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.(c) Determine the behavior of
A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are made of material that costs 60 per square centimeter, while the sides are
In physics, it is established that the acceleration due to gravity, g (in m/sec2),at a height h meters above sea level is given bywhere 6.374 Ã— 106 is the radius of Earth in meters.(a)
In problem, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers.f(x) = 4x4 + 5x3 + 9x2 + 10x + 2
In problem, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.F(x) = x4- 16/x2 - 2x
In problem, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers.f(x) = x3 - x2 - 10x - 8
In problem, solve each inequality algebraically.x – 1/x + 2 ≥ -2
In problem, for each polynomial function:(a) List each real zero and its multiplicity.(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.(c) Determine the behavior of
In problem, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers.f(x) = x4 - x3 - 6x2 + 4x + 8
United Parcel Service has contracted you to design an open box with a square base that has a volume of 5000 cubic inches. See the illustration.(a) Express the surface area S of the box as a function
In problem, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.G(x) = x4- 1/x2 - x
In problem, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers.f(x) = x3 - 3x2 - 6x + 8
In problem, solve each inequality algebraically.x + 1/x - 3 ≤ 2
In problem, for each polynomial function:(a) List each real zero and its multiplicity.(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.(c) Determine the behavior of
In problem, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers.f(x) = x4 + x3 - 3x2 - x + 2
United Parcel Service has contracted you to design a closed box with a square base that has a volume of 10,000 cubic inches. See the illustration.(a) Express the surface area S of the box as a
The Doppler effect (named after Christian Doppler) is the change in the pitch (frequency) of the sound from a source (s) as heard by an observer (0) when one or both are in motion. If we assume both
In problem, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. 8x2 + 26х — 7 4х — 1 R(x)
List all the potential rational zeros of f(x) = -6x5 + x4 + 2x3 - x + 1.
In problem, solve each inequality algebraically.x2 + 3x ≥ 10
In problem, for each polynomial function:(a) List each real zero and its multiplicity.(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.(c) Determine the behavior of
In problem, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers.f(x) = 2x4 - x3 - 5x2 + 2x + 2
A rectangular area adjacent to a river is to be fenced in; no fence is needed on the river side. The enclosed area is to be 1000 square feet. Fencing for the side parallel to the river is $5 per
In problem, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. + 7x – 5 R(x) Зх + 5
In problem, solve each inequality algebraically.7x - 4 ≥ -2x2
In problem, find the remainder R when f(x) is divided by g(x). Is g a factor of f?f(x) = x4 - 2x3 + 15x - 2; g(x) = x + 2
In problem, find the complex zeros of each polynomial function. Write f in factored form.f(x) = 3x4 - x3 - 9x2 + 159x – 52
In problem, solve each inequality algebraically. x + 4 - 2 VI
In problem, follow Steps 1 through 8 to analyze the graph of each function.f(x) = x + 1/x
In problem, use transformations of the graph of y = x4 or y – x5 to graph each function.f(x) = 4 - (x - 2)5
In problem, graph each rational function using transformations.R(x) = 1/x – 1 + 1
In problem, list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.f(x) = 6x4 - x2 + 2
In problem, solve each inequality. Graph the solution set. -2 1 - 3x
In problem, find the complex zeros of each polynomial function. Write f in factored form.f(x) = x4 + 3x3 - 19x2 + 27x - 252
In problem, solve each inequality algebraically. (x + 5)² x2 - 4 х
In problem, follow Steps 1 through 8 to analyze the graph of each function.R(x) = x2 + x - 30/x + 6
In problem, use transformations of the graph of y = x4 or y – x5 to graph each function.f(x) = 1/2 (x - 1)5 - 2
In problem, graph each rational function using transformations. -1 R(x) x² + 4x + 4 2
In problem, list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.f(x) = -4x3 - x2 + x + 2
In problem, solve each inequality. Graph the solution set. 2 1 x + 3
In problem, find the complex zeros of each polynomial function. Write f in factored form.f(x) = x4 + 2x3 + 22x2 + 50x – 75
In problem, solve each inequality algebraically. (x – 2)? x? - 1
In problem, follow Steps 1 through 8 to analyze the graph of each function.R(x) = x2 + 5x + 6/x + 3
In problem, use transformations of the graph of y = x4 or y – x5 to graph each function.f(x) = 2(x + 1)4 + 1
In problem, graph each rational function using transformations.G(x) = 2/(x + 2)2
In problem, list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.f(x) = 2x5 - x4 - x2 + 1

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