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mathematics
precalculus

Questions and Answers of Precalculus

If f(x) = -2x5 + x3 - 5x2 + 7, then limx→∞ f(x) = ________ and limx→∞ f(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) = 3x4 - 6x3 - 5x + 10; x –
Solve: x + 2/x – 3 < 2
Find an equation of the line perpendicular to 3x - 2y = 7 that contains the point (1, 5).
If r is a solution to the equation f(x) = 0, name three additional statements that can be made about f and r assuming f is a polynomial function.
Find the intercepts of the graph of the equation y = x2 -1/x2 – 4.
In problem, find the quadratic function for which:Vertex is (-1, 2); contains the point (1, 6)
In problem,(a) Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any.(b) Determine the
In problem, determine whether the given function is linear or nonlinear. If it is linear, determine the slope. x ………………… y = f(x)-2 ………………………. 4-1
In problem,(a) Draw a scatter diagram.(b) Select two points from the scatter diagram and find the equation of the line containing the points selected.(c) Graph the line found in part (b) on the
Solve x2 - 10x + 24 ≥ 0.
Solve: 60x - 900 = -15x + 2850.
Graph y = 2x - 3.
In problem, use the graph shown to find(a) The domain and range of each function(b) The intercepts, if any(c) Horizontal asymptotes, if any(d) Vertical asymptotes, if any(e) Oblique asymptotes, if
In problem, tell the maximum number of real zeros that each polynomial function may have. Do not attempt to find the zeros.f(x) = x5 - x4 + x3 - x2 + x – 1
In problem, discuss each rational function following the eight steps. Зx3 F(x) (х — 1)2
In problem, follow Steps 1 through 8 to analyze the graph of each function.G(x) = x2 - x - 12/x + 1
In problem, use the given zero to find the remaining zeros of each function.g(x) = 2x2 - 3x4 – 5x2 - 15x2 - 207x + 108; zero: 3i
In problem, use the graph shown to find(a) The domain and range of each function(b) The intercepts, if any(c) Horizontal asymptotes, if any(d) Vertical asymptotes, if any(e) Oblique asymptotes, if
In problem, tell the maximum number of real zeros that each polynomial function may have. Do not attempt to find the zeros.f(x) = x5 - x4 + x3 - x2 + x – 1
In problem, follow Steps 1 through 8 to analyze the graph of each function.F(x) = x2 + x - 12/x + 2
In problem, solve each inequality algebraically.x4 > x2
In problem, use the given zero to find the remaining zeros of each function.h(x) = 3x5 + 2x4 + 15x2 + 10x2 - 528x - 352; zero: -4i
In problem, use transformations of the graph of y = x4 or y – x5 to graph each function.f(x) = (x - 2)5
In problem, use the graph shown to find(a) The domain and range of each function(b) The intercepts, if any(c) Horizontal asymptotes, if any(d) Vertical asymptotes, if any(e) Oblique asymptotes, if
In problem, tell the maximum number of real zeros that each polynomial function may have. Do not attempt to find the zeros.f(x) = x4 + 5x3 – 2
In problem, discuss each rational function following the eight steps. х2 — бх + 9 х2 R(x)
In problem, follow Steps 1 through 8 to analyze the graph of each function.R(x) = x2 - x - 12/x + 5
In problem, solve each inequality algebraically.x3 + 2x2 - 3x > 0
In problem, use the given zero to find the remaining zeros of each function.f(x) = x4 - 7x3 + 14x2 - 38x - 60; zero: 1 + 3i
In problem, use transformations of the graph of y = x4 or y – x5 to graph each function.f(x) = (x +1)4
In problem, use the graph shown to find(a) The domain and range of each function(b) The intercepts, if any(c) Horizontal asymptotes, if any(d) Vertical asymptotes, if any(e) Oblique asymptotes, if
In problem, tell the maximum number of real zeros that each polynomial function may have. Do not attempt to find the zeros.f(x) = -x4 + x2 – 1
In problem, follow Steps 1 through 8 to analyze the graph of each function.R(x) = x2 + 3x - 12/x - 4
In problem, solve each inequality algebraically.x3 - 2x2 - 3x > 0
In problem, use the given zero to find the remaining zeros of each function.h(x) = x4 - 9x3 + 21x2 + 21x - 130; zero: 3 - 2i
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) = -3x2(x + 2)3
In problem, tell the maximum number of real zeros that each polynomial function may have. Do not attempt to find the zeros.f(x) = -x3 - x2 + x + 1
In problem, use the graph shown to find(a) The domain and range of each function(b) The intercepts, if any(c) Horizontal asymptotes, if any(d) Vertical asymptotes, if any(e) Oblique asymptotes, if
In problem, discuss each rational function following the eight steps. х H(х) .2 х — 1
In problem, follow Steps 1 through 8 to analyze the graph of each function.F(x) = x2 + 3x + 2/x - 1
In problem, solve each inequality algebraically.(x + 1)(x + 2)(x + 3) ≤ 0
In problem, use the given zero to find the remaining zeros of each function.h(x) = 3x4 + 5x3 + 25x2 + 45x - 18; zero: 3i
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) = 2(x - 1)2(x2 + 1)
In problem, tell the maximum number of real zeros that each polynomial function may have. Do not attempt to find the zeros.f(x) = 3x3 - 2x2 + x + 2
In problem, use the graph shown to find(a) The domain and range of each function(b) The intercepts, if any(c) Horizontal asymptotes, if any(d) Vertical asymptotes, if any(e) Oblique asymptotes, if
In problem, solve each inequality algebraically.(x - 1)(x - 2)(x - 3) ≤ 0
In problem, use the given zero to find the remaining zeros of each function.f(x) = 2x4 + 5x3 + 5x2 + 20x - 12; zero: -2i
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) - x2 – 5/x3
In problem, tell the maximum number of real zeros that each polynomial function may have. Do not attempt to find the zeros.f(x) = -3x5 + 4x4 + 2
In problem, find the domain of each rational function. -2(x² – 4) 3(x² + 4x + 4) F(x) :
In problem, discuss each rational function following the eight steps. R(x) 4 - x
In problem, solve each inequality algebraically.3x3 < -15x2
In problem, follow Steps 1 through 8 to analyze the graph of each function.H(x) = x2 + 4/x4 - 1
In problem, use the given zero to find the remaining zeros of each function.g(x) = x3 + 3x2 + 25x + 75; zero: -5i
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) = 5x4 – πx3 + 1/2
Suppose that f(x) = x2 - 5x + 1 and g(x) = -4x - 7.(a) Find f + g and state its domain.(b) Find f/g and state its domain.
In problem, tell the maximum number of real zeros that each polynomial function may have. Do not attempt to find the zeros.f(x) = 2x6 - 3x2 - x + 1
In problem, discuss each rational function following the eight steps. 2х — 6 R(x) = х
In problem, solve each inequality algebraically.2x3 > -8x2
In problem, follow Steps 1 through 8 to analyze the graph of each function.H(x) = x2 – 1/x4 - 16
In problem, use the given zero to find the remaining zeros of each function.f(x) = x3 - 4x2 + 4x - 16; zero: 2i
In problem, form a polynomial function f(x) with real coefficients having the given degree and zeros.Degree 5; zeros: 1,multiplicity 3; 1 + i
In problem, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.h(x) = √x(√x - 1)
Graph the function f(x) = -3(x + 1)2 + 5 using transformations.
In problem, tell the maximum number of real zeros that each polynomial function may have. Do not attempt to find the zeros.f(x) = 5x4 + 2x2 - 6x – 5
In problem, find the domain of each rational function.H(x) = x - 3/x4 + 1
In problem, find the domain of each rational function. Find any horizontal, vertical, or oblique asymptotes. R(x) = x x - 1
In problem, solve each inequality algebraically.x3 + 8x2 < 0
In problem, follow Steps 1 through 8 to analyze the graph of each function.R(x) = -4/(x + 1)(x2 - 9)
In problem, form a polynomial function f(x) with real coefficients having the given degree and zeros.Degree 4; zeros: 3,multiplicity 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.g(x) = x3/2 - x2 + 2
For the function(a) Find the domain of f.(b) Locate any intercepts.(c) Graph the function.(d) Based on the graph, find the range. (2x+1 f(x)= if –3
In problem, tell the maximum number of real zeros that each polynomial function may have. Do not attempt to find the zeros.f(x) = -4x7 + x3 - x2 + 2
In problem, find the domain of each rational function.H(x) = 3x2 + x/x2 + 4
In problem, find the domain of each rational function. Find any horizontal, vertical, or oblique asymptotes. x + 3x + 2 (x + 2)² |R(x)
In problem, solve each inequality algebraically.x3 - 4x2 > 0
In problem, form a polynomial function f(x) with real coefficients having the given degree and zeros.Degree 6; zeros: i, 4 - i; 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) = x(x - 1)
Determine algebraically whether the functionis even, odd, or neither. 5x f(x) x2 - 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) = 3x4 + x3 - 3x + 1; x + 1/3
In problem, find the domain of each rational function.R(x) = x/x4 - 1
In problem, find the domain of each rational function. Find any horizontal, vertical, or oblique asymptotes. R(x) = x + 4 x-2
In problem, solve each inequality algebraically.(x - 5)(x + 2)2 > 0
In problem, follow Steps 1 through 8 to analyze the graph of each function.G(x) = 3x/x2 - 1
In problem, form a polynomial function f(x) with real coefficients having the given degree and zeros.Degree 5; zeros: 2; -i; 1 + 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) = 1 – 1/x
In parts (a) to (f), use the following graph.(a) Determine the intercepts.(b) Based on the graph, tell whether the graph is symmetric with respect to the x-axis, the y-axis, and/or the origin.(c)
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) = 2x4 - x3 + 2x - 1; x – ½
In problem, find the domain of each rational function.R(x) = x/x3 - 8
In problem, find the domain of each rational function. Find any horizontal, vertical, or oblique asymptotes. |R(x) = 9. x² – 9
In problem, solve each inequality algebraically.(x - 5)2(x + 2) < 0
In problem, follow Steps 1 through 8 to analyze the graph of each function.G(x) = x/x2 - 4
In problem, form a polynomial function f(x) with real coefficients having the given degree and zeros.Degree 4; zeros: i, 1 + 2i
In problem, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.h(x) = 3 – 1/2x
Find the average rate of change of f(x) = x2 + 3x + 1 from 1 to 2. Use this result to find the equation of the secant line containing (1, f (1)) and (2,f(2)).
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) = x6 - 16x4 + x2 - 16; x + 4
In problem, find the domain of each rational function. Q(x) = -x(1-x) 3x + 5x - 2
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = (x - 4)(x + 2)2(x - 2)
In problem, solve the inequality by using the graph of the function.Solve R(x) ≥ 0, where R(x) = 2x + 4/x - 1.

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