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mathematics
precalculus

Questions and Answers of Precalculus

In problem, follow Steps 1 through 8 to analyze the graph of each function.R(x) = x2 + x – 12/x2 - 4
In problem, form a polynomial function f(x) with real coefficients having the given degree and zeros.Degree 4; zeros: 3 + 2i; 4,multiplicity 2
In problem, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.g(x) = 1 - x2/2
Graph f(x) = 2x2 - 4x + 1 by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any.
In problem, find the domain of each rational function. F(x) 3x(x - 1) 2x5x3
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = (x - 1)2(x + 3)(x + 1)
In problem, solve the inequality by using the graph of the function.Solve R(x) ≤ 0, where R(x) = 3x + 3/2x + 4.
In problem, follow Steps 1 through 8 to analyze the graph of each function.R(x) = x2/x2 + x - 6
In problem, information is given about a polynomial function f(x) whose coefficients are real numbers. Find the remaining zeros of f.Degree 6; zeros: i, 3 - 2i, -2 + i
In problem, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.f(x) = 5x2 + 4x4
Graph the function f(x) = -3x + 7.
In problem, use the Remainder Theorem to find the remainder when f(x) is divided by x - c. Then use the Factor Theorem to determine whether x - c is a factor of f(x).f(x) = 2x6 - 18x4 + x2 - 9; x + 3
In problem, find the domain of each rational function. G(x) = 6 (x + 3) (4 - x)
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = -4x3 + 4x
In problem, solve the inequality by using the graph of the function.Solve R(x) < 0, where R(x) = x/(x - 1)(x + 2)
In problem, follow Steps 1 through 8 to analyze the graph of each function.G(x) = x3 + 1/x2 + 2x
In problem, information is given about a polynomial function f(x) whose coefficients are real numbers. Find the remaining zeros of f.Degree 6; zeros: 2, 2 + i, -3 - i, 0
In problem, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.f(x) = 4x + x3
Answer the following questions regarding the function(a) What is the domain of f?(b) Is the point (2, 6) on the graph of f?(c) If x = 3, what is f(x)? What point is on the graph of f?(d) If f(x) = 9,
In problem, use the Remainder Theorem to find the remainder when f(x) is divided by x - c. Then use the Factor Theorem to determine whether x - c is a factor of f(x).f(x) = 3x6 + 82x3 + 27; x + 3
In problem, find the domain of each rational function. -4x? (х — 2)(х + 4) Н(х)
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = -2x3 + 4x2
In problem, solve the inequality by using the graph of the function.Solve R(x) > 0, where R(x) = x + 1/x(x + 4).
In problem, follow Steps 1 through 8 to analyze the graph of each function.H(x) = x3 – 1/x2 - 9
Explain what the notation limx→∞ f(x) = -∞ means.
For the function f(x) = x2+ 5x - 2, find(a) f(3)(b) f(-x)(c) -f(x)(d) f(3x)(e) f(x + h) – f(x) -h + 0
In problem, use the Remainder Theorem to find the remainder when f(x) is divided by x - c. Then use the Factor Theorem to determine whether x - c is a factor of f(x).f(x) = 4x4 - 15x2 - 4; x - 2
In problem, find the domain of each rational function.R(x) = 5x2/3 + x
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = (x - 2)(x + 4)2
In problem, solve the inequality by using the graph of the function.Solve f(x) < 0, where f(x) = -1/2(x + 4)(x - 1)3.
In problem, follow Steps 1 through 8 to analyze the graph of each function.Q(x) = x4 – 1/x2 - 4
In problem, information is given about a polynomial function f(x) whose coefficients are real numbers. Find the remaining zeros of f.Degree 4; zeros: i, 2, -2
Is the following the graph of a function? Why or why not? y.
In problem, find the domain of each rational function.R(x) = 4x/x - 3
In problem, solve the inequality by using the graph of the function.Solve f(x) ≤ 0, where f(x) = -2(x + 2)(x - 2)3.
In problem, follow Steps 1 through 8 to analyze the graph of each function. x* + x² + 1 P(x) : x² – 1
In problem, information is given about a polynomial function f(x) whose coefficients are real numbers. Find the remaining zeros of f.Degree 5; zeros: 0, 1, 2, i
The graph of the function f(x) = 3x4 - x3 + 5x2 - 2x - 7 will behave like the graph of for large values of |x|.
In problem, use the Remainder Theorem to find the remainder when f(x) is divided by x - c. Then use the Factor Theorem to determine whether x - c is a factor of f(x).f(x) = -4x3 + 5x2 + 8; x + 3
True or False If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients gives rise to the horizontal asymptote.
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = (x - 2)2(x + 4)
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = x(x - 2)(x - 4)
In problem, solve the inequality by using the graph of the function.Solve f(x) > 0, where f(x) = (x - 1)(x + 3)2.
In problem, follow Steps 1 through 8 to analyze the graph of each function.R(x) = 6/x2 – x - 6
Graph y = 1/x.
If the numerator and the denominator of a rational function have no common factors, the rational function is ____ ______ _______.
In problem, information is given about a polynomial function f(x) whose coefficients are real numbers. Find the remaining zeros of f.Degree 5; zeros: 1, i, 2i
The points at which a graph changes direction (from increasing to decreasing or decreasing to increasing) are called ____________.
In problem, use the Remainder Theorem to find the remainder when f(x) is divided by x - c. Then use the Factor Theorem to determine whether x - c is a factor of f(x).f(x) = 4x3 - 3x2 - 8x + 4; x – 2
For the equation y = x3 - 9x, determine the intercepts and test for symmetry.
If a rational function is proper, then _____________ is a horizontal asymptote.
In problem, for the given functions and , find:(a) (f ° g)(4)(b) (g ° f)(2)(c) (f ° f)(1)(d) (g ° g)(0)f(x) = 2x; g(x) = 3x2 + 1
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = x(x + 2)(x + 4)
In problem, solve the inequality by using the graph of the function.Solve f(x) ≥ 0, where f(x) = (x + 4)(x - 2)2.
In problem, follow Steps 1 through 8 to analyze the graph of each function.R(x) = 3/x2 - 4
In problem, information is given about a polynomial function f(x) whose coefficients are real numbers. Find the remaining zeros of f.Degree 4; zeros: 1, 2, 2 + i
True or False If f is a polynomial function of degree 4 and if f(2) = 5, then where p(x) is a polynomial of degree 3. f(x) p(x) x - 2 x - 2
Find the center and radius of the circle x2 + 4x + y2 - 2y -4 = 0. Graph the circle.
Use the Intermediate Value Theorem to show that the function f(x) = -2x2 - 3x + 8 has at least one real zero on the interval [0, 4].
True or FalseThe graph of a rational function may intersect a vertical asymptote.
In problem, evaluate each expression using the graphs of y = f (x) and y = g(x) shown in the figure.(a) (g ° f)(1)(b) (g ° f)(5)(c) (f ° g)(0)(d) (f ° g)(2) УА y = g (x) (6, 5) (7,
In problem, solve the inequality by using the graph of the function.Solve f(x) ≤ 0, where f(x) = x(x + 2)2.
In problem, graph each function using transformations (shifting, compressing, stretching, and reflection). Show all the stages.f(x) = (1 - x)3
In problem, follow Steps 1 through 8 to analyze the graph of each function.R(x) = 2x + 4/x - 1
In problem, information is given about a polynomial function f(x) whose coefficients are real numbers. Find the remaining zeros of f.Degree 4; zeros: i, 1 + i
The graphs of power functions of the form f(x) = xn, where n is an even integer, always contain the points ______, ________, and ___________.
If f is a polynomial function and x - 4 is a factor of f, then f(4) = _______.
Solve the inequality 3x + 2 ≤ 5x - 1 and graph the solution set.
True or FalseThe graph of a rational function may intersect a horizontal asymptote.
In problem, write a function that meets the given conditions.Rational function; asymptotes: y = 2, x = 4; domain: {xlx ≠ 4, x ≠ 9}.
In problem, evaluate each expression using the graphs of y = f (x) and y = g(x) shown in the figure.(a) (g ° f)(-1)(b) (g ° f)(0)(c) (f ° g)(-1)(d) (f ° g)(4) УА y = g (x) (6, 5)
In problem, solve the inequality by using the graph of the function.Solve f(x) < 0, where f(x) = x2(x - 3).
In problem, graph each function using transformations (shifting, compressing, stretching, and reflection). Show all the stages.f(x) = (x - 1)4 + 2
In problem, follow Steps 1 through 8 to analyze the graph of each function.R(x) = 3x + 3/2x + 4
In problem, information is given about a polynomial function f(x) whose coefficients are real numbers. Find the remaining zeros of f.Degree 3; zeros: 4, 3 + i
In problem, use the graph of the function f to solve the inequality.(a) f(x) > 0(b) f(x) ‰¤ 0 3 y = 1 3 4 5 x -4 -3 -2 -2 x= 2 X=-1
If r is a real zero of even multiplicity of a function f, then the graph of f _______ (crosses/touches) the x-axis at r.
True or FalseEvery polynomial function of degree 3 with real coefficients has exactly three real zeros.
Solve the equation x3 – 6x2 + 8x = 0.
For a rational function R, if the degree of the numerator is less than the degree of the denominator, then R is _________.
In problem, write a function that meets the given conditions.Fourth-degree polynomial with real coefficients; zeros: -2, 0, 3 + i.
In problem, evaluate each expression using the values given in the table.(a) (f ° g)(1)(b) (f ° g)(2)(c) (g ° f)(2)(d) (g ° f)(3)(e) (g ° g)(1)(f) (f ° f)(3) 3 1 х -3 -2 -1
In problem, graph each function using transformations (shifting, compressing, stretching, and reflection). Show all the stages.f(x) = (x - 1)4 – 2
In problem, follow Steps 1 through 8 to analyze the graph of each function. %3D (x – 1)(x + 2) |R(x)
In problem, follow Steps 1 through 8 to analyze the graph of each function.R(x) = x + 1/x(x + 4)
In problem, information is given about a polynomial function f(x) whose coefficients are real numbers. Find the remaining zeros of f.Degree 3; zeros: 3, 4 - i
In problem, use the graph of the function f to solve the inequality.(a) f(x) < 0(b) f(x) ‰¥ 0 X = -1 x = 1 y = 0 -3 3
The graph of every polynomial function is both ________ and ______.
If a function f, whose domain is all real numbers, is even and if 4 is a zero of f, then ________ is also a zero.
Does the relation ((3, 6), (1, 3), (2, 5), (3, 8)} represent a function? Why or why not?
If, as x approaches some number c, the values of |R(x)| → ∞, then the line x = c is a ________ of the graph of R.
Sketch the graph of the function in Problem 6. Label all intercepts, vertical asymptotes, horizontal asymptotes, and oblique asymptotes.Data from problem 6 х2 + 2х - 3 r(x) х+1
In problem, evaluate each expression using the values given in the table.(a) (f ° g)(1)(b) (f ° g)( -1)(c) (g ° f)(-1)(d) (g ° f)(0)(e) (g ° g)( -2)(f) (f ° f)(-1) -3 -1 3 х
In problem, graph each function using transformations (shifting, compressing, stretching, and reflection). Show all the stages.f(x) = -(x - 1)4
In problem, graph each function using transformations (shifting, compressing, stretching, and reflection). Show all the stages.f(x) = -x3 + 3
(a) Find the domain of R.(b) Find the x-intercepts of R.R(x) = x(x - 2)2/x – 2
In problem, use the graph of the function f to solve the inequality.(a) f(x) < 0(b) f(x) ‰¥ 0 y. 2 -2 3 -1 -2
If g(5) = 0, what point is on the graph of g? What is the corresponding x-intercept of the graph of g?
When a polynomial function f is divided by x - c, the remainder is _______.
Graph the equation y = x3.

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