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mathematics
precalculus 1st
Precalculus 1st Edition Jay Abramson - Solutions
For the following exercises, determine whether the graph of the function provided is a graph of a polynomial function. If so, determine the number of turning points and the least possible degree for the function. X
For the following exercises, find the slant asymptote. f(x) = x²2 - 1 x + 2
For the following exercises, perform the indicated operation and express the result as a simplified complex number.i8
For the following exercises, determine whether the graph of the function provided is a graph of a polynomial function. If so, determine the number of turning points and the least possible degree for the function. X
For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. q(x) = x-5 3x - 1
For the following exercises, find the inverse of the function and graph both the function and its inverse.f(x) = 2/x
For the following exercises, use the given information to find the unknown value.y varies jointly as the square of x and of z and inversely as the square root of w and of t. When x = 2, z = 3, w = 16, and t = 3, then y = 1. Find y when x = 3, z = 2, w = 36, and t = 5.
For the following exercises, find all complex solutions (real and non-real). x3 + x2 + x + 1 = 0
For the following exercises, use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization.x + 3, −4x3 + 5x2 + 8
For the following exercises, perform the indicated operation and express the result as a simplified complex number. 4+ V-20 2
For the following exercises, find the zeros and give the multiplicity of each.f(x) = 2x4 (x3 − 4x2 + 4x)
For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. s(x) 4 = (x - 2)²
For the following exercises, find all complex solutions (real and non-real).x3 − 8x2 + 25x − 26 = 0
For the following exercises, use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization.x − 2, 4x4 − 15x2 − 4
For the following exercises, find the zeros and give the multiplicity of each.f(x) = 4x4 (9x4 − 12x3 + 4x2 )
For the following exercises, find the slant asymptote. f(x) = 2x³ - x² + 4 x² + 1
For the following exercises, determine whether the graph of the function provided is a graph of a polynomial function. If so, determine the number of turning points and the least possible degree for the function. X
For the following exercises, perform the indicated operation and express the result as a simplified complex number.i15
For the following exercises, use a graph to help determine the domain of the functions. f(x)=1 (x + 1)(x - 1) X
For the following exercises, solve the equations over the complex numbers.2x2 − 6x + 5 = 0
For the following exercises, use a calculator to graph the equation implied by the given variation.y varies directly as the cube of x and when x = 2, y = 4.
For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. r(x) = 5 (x + 1)²
For the following exercises, use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization. x-1727₁ 2x² X ,2x¹-x²+2x-1
For the following exercises, find all complex solutions (real and non-real).x3 + 13x2 + 57x + 85 = 0
For the following exercises, graph the polynomial functions. Note x- and y-intercepts, multiplicity, and end behavior.f(x) = (x + 3)2 (x − 2)
For the following exercises, find the inverse of the function with the domain given. f(x) = (x - 2)², x ≥ 2
For the following exercises, use a graph to help determine the domain of the functions. f(x)=√ (x + 2)(x-3) x-1
For the following exercises, perform the indicated operation and express the result as a simplified complex number.i22
For the following exercises, determine whether the graph of the function provided is a graph of a polynomial function. If so, determine the number of turning points and the least possible degree for the function. x
For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. f(x) = 3x²14x - 5 3x² + 8x - 16
For the following exercises, solve the equations over the complex numbers.x2 + x + 2 = 0
For the following exercises, use a calculator to graph the equation implied by the given variation.y varies directly as the square root of x and when x = 36, y = 2.
For the following exercises, use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization. x+3,3x² + x²-3x+1
For the following exercises, find all complex solutions (real and non-real).3x3 − 4x2 + 11x + 10 = 0
For the following exercises, graph the polynomial functions. Note x- and y-intercepts, multiplicity, and end behavior.g(x) = (x + 4)(x − 1)2
For the following exercises, use a calculator to help answer the questions.Evaluate (1 + i)k for k = 4, 8, and 12. Predict the value if k = 16.
For the following exercises, use a graph to help determine the domain of the functions. f(x) = = x(x + 3) x-4
For the following exercises, find the inverse of the function with the domain given.f(x) = (x + 4)2 − 3, x ≥ −4
For the following exercises, determine whether the graph of the function provided is a graph of a polynomial function. If so, determine the number of turning points and the least possible degree for the function. y - Х
For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. g(x) = 2x² + 7x - 15 3x² - 14+ 15
For the following exercises, solve the equations over the complex numbers.x2 − 2x + 4 = 0
For the following exercises, use a calculator to graph the equation implied by the given variation.y varies inversely with x and when x = 6, y = 2.
For the following exercises, use the graph of the third-degree polynomial and one factor to write the factored form of the polynomial suggested by the graph. The leading coefficient is one.Factor is x2 − x + 3 ***** maifige 81 II
For the following exercises, find all complex solutions (real and non-real).x4 + 2x3 + 22x2 + 50x − 75 = 0
For the following exercises, graph the polynomial functions. Note x- and y-intercepts, multiplicity, and end behavior.h(x) = (x − 1)3 (x + 3)2
For the following exercises, use a calculator to help answer the questions.Evaluate (1 − i)k for k = 2, 6, and 10. Predict the value if k = 14.
For the following exercises, find the inverse of the function with the domain given.f(x) = x2 + 6x − 2, x ≥ −3
For the following exercises, use a graph to help determine the domain of the functions. f(x) = V x²-x-20 x-2
For the following exercises, determine whether the graph of the function provided is a graph of a polynomial function. If so, determine the number of turning points and the least possible degree for the function. x+
For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function. (h, k) = (2, 0), (x, y) = (4, 4)
For the following exercises, use a calculator to graph the equation implied by the given variation.y varies inversely as the square of x and when x = 1, y = 4.
For the following exercises, use the graph of the third-degree polynomial and one factor to write the factored form of the polynomial suggested by the graph. The leading coefficient is one.Factor is x2 + 2x + 4 ma 81 I type I x
For the following exercises, find all complex solutions (real and non-real).2x3 − 3x2 + 32x + 17 = 0
For the following exercises, graph the polynomial functions. Note x- and y-intercepts, multiplicity, and end behavior.k(x) = (x − 3)3 (x − 2)2
For the following exercises, use a graph to help determine the domain of the functions. f(x)=√ 9-x² x +4
For the following exercises, use a calculator to help answer the questions.Evaluate (1 + i)k − (1 − i)k for k = 4, 8, and 12 . Predict the value for k = 16.
For the following exercises, find the inverse of the function with the domain given.f(x) = 2x3 − 3
For the following exercises, make a table to confirm the end behavior of the function.f(x) = −x3
For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function. (h, k) = (−2, −1), (x, y) = (−4, 3)
For the following exercises, use Kepler’s Law, which states that the square of the time, T, required for a planet to orbit the Sun varies directly with the cube of the mean distance, a, that the planet is from the Sun.Using the Earth’s time of 1 year and mean distance of 93 million miles, find
For the following exercises, use the graph of the third-degree polynomial and one factor to write the factored form of the polynomial suggested by the graph. The leading coefficient is one.Factor is x2 + x + 1 y 60- annanna 20- 20-
For the following exercises, use a calculator to help answer the questions. Show that a solution of x-1=0 is V2 2 + Vi i. 2
For the following exercises, use the graph of the third-degree polynomial and one factor to write the factored form of the polynomial suggested by the graph. The leading coefficient is one.Factor is x2 + 2x + 5 Sub augham DE 10 30- HE
For the following exercises, find the inverse of the function with the domain given. f(x)=√4x + 5-3
For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. b(x) 9-x-zx 7 - x2 – 4
For the following exercises, find the inverse of the function with the domain given. f(x)= x-3 2x + 1
For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. h(x) = = 2x² + x1 x-4
For the following exercises, use a calculator to help answer the questions.Show that a solution of x6 + 1 = 0 is √3/2 +1/2 i.
For the following exercises, use a calculator to graph the function. Then, using the graph, give three points on the graph of the inverse with y-coordinates given.f(x) = x3 + x − 2, y = 0, 1, 2
For the following exercises, use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm which of those possibilities is the actual combination.f(x) = x4 − x2 − 1
For the following exercises, use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm which of those possibilities is the actual combination.f(x) = x3 − 1
For the following exercises, use a calculator to graph the function. Then, using the graph, give three points on the graph of the inverse with y-coordinates given.f(x) = x3 − x − 2, y = 1, 2, 3
For the following exercises, use Kepler’s Law, which states that the square of the time, T, required for a planet to orbit the Sun varies directly with the cube of the mean distance, a, that the planet is from the Sun.Use the result from the previous exercise to determine the time required for
For the following exercises, make a table to confirm the end behavior of the function.f(x) = x4 − 5x2
For the following exercises, graph the polynomial functions. Note x- and y-intercepts, multiplicity, and end behavior.m(x) = −2x(x − 1)(x + 3)
For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function.(h, k) = (0, 1), (x, y) = (2, 5)
For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function.(h, k) = (2, 3), (x, y) = (5, 12)
For the following exercises, use Kepler’s Law, which states that the square of the time, T, required for a planet to orbit the Sun varies directly with the cube of the mean distance, a, that the planet is from the Sun.Using Earth’s distance of 150 million kilometers, find the equation relating
For the following exercises, make a table to confirm the end behavior of the function.f(x) = (x − 1)(x − 2)(3 − x)
For the following exercises, find the inverse of the functions. f(x) = x² + 2x, [-1, ∞)
For the following exercises, use synthetic division to find the quotient. If the divisor is a factor, then write the factored form. - x³ + 4x + 10 x - 3
For the following exercises, write an equation describing the relationship of the given variables.y varies jointly as x and z and inversely as the square root of w and the square of t. When x = 3, z = 1, w = 25, and t = 2, then y = 6.
For the following exercises, perform the indicated operation and express the result as a simplified complex number.(4 − 2i)(4 + 2i)
For the following exercises, describe the local and end behavior of the functions. f(x) = 2x² 32 - 6x² + 13x - 5
For the following exercises, find the intercepts of the functions.f(x) = x(x2 − 2x − 8)
For the following exercises, solve the equations over the complex numbers.x2 + 27 = 0
For the following exercises, use the given information to find the unknown value.y varies inversely with x. When x = 3, then y = 2. Find y when x = 1.
For the following exercises, use synthetic division to find the quotient. If the divisor is a factor, then write the factored form. 2x³ + 6x² 11x - 12 - x + 4
For the following exercises, find the inverse of the functions. f(x) = x² + 4x + 1, [−2, ∞)
For the following exercises, use the Rational Zero Theorem to find all real zeros.2x3 − 3x2 − x + 1 = 0
For the following exercises, find the slant asymptote of the functions. f(x) = 24x² + 6x 2x+1
For the following exercises, use synthetic division to find the quotient.(x4 + x3 − 3x2 − 2x + 1) ÷ (x + 1)
For the following exercises, use the Intermediate Value Theorem to confirm that the given polynomial has at least one zero within the given interval.f(x) = x3 − 100x + 2, between x = 0.01 and x = 0.1
For the following exercises, perform the indicated operation and express the result as a simplified complex number.(3 + 4i)(3 − 4i)
For the following exercises, use synthetic division to find the quotient. If the divisor is a factor, then write the factored form. 3x² + 3x³ + 2x + 2 x + 1
For the following exercises, determine the least possible degree of the polynomial function shown. y H 2 3/4 5 X
For the following exercises, solve the equations over the complex numbers.x2 + 2x + 5 = 0
For the following exercises, find the intercepts of the functions. f(x) = (x + 3)(4x2 − 1)
For the following exercises, find the inverse of the functions. f(x)=x² - 6x + 3, [3, ∞)
For the following exercises, use the given information to find the unknown value.y varies inversely with the square of x. When x = 4, then y = 3. Find y when x = 2.
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