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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

For the following exercises, find the inverse of the functions with a, b, c positive real numbers. f(x) = Vax² + b
For the following exercises, evaluate the expressions, writing the result as a simplified complex number. (1 + 3i)(2 - 4i) (1 + 2i)
For the following exercises, sketch a graph of the quadratic function and give the vertex, axis of symmetry, and intercepts.f(x) = x2 − 6x − 1
For the following exercises, graph the polynomial functions using a calculator. Based on the graph, determine the intercepts and the end behavior.f(x) = x(14 − 2x)(10 − 2x)2
For the following exercises, use a calculator with CAS to answer the questions. Consider x-1 x-1 expect the result to be if k= 4? with k = 1, 2, 3. What do you
For the following exercises, use the graph to identify zeros and multiplicity. III x II ingen ngungu 24 I
For the following exercises, use the given information to answer the questions.The volume of a gas held at constant temperature varies indirectly as the pressure of the gas. If the volume of a gas is
For the following exercises, use a calculator with CAS to answer the questions. Consider +1 x² x + 1 the result to be if k = 7? for k= 1, 3, 5. What do you expect
For the following exercises, write an equation for a rational function with the given characteristics.Vertical asymptotes at x = −3 and x = 6, x-intercepts at (−2, 0) and (1, 0), horizontal
For the following exercises, evaluate the expressions, writing the result as a simplified complex number. (3 + 1)² (1 + 2i)²
For the following exercises, find the inverse of the functions with a, b, c positive real numbers. f(x) = ax + b
For the following exercises, graph the polynomial functions using a calculator. Based on the graph, determine the intercepts and the end behavior.f(x) = x3 − 16x
For the following exercises, use the given information to answer the questions.The weight of an object above the surface of the Earth varies inversely with the square of the distance from the center
For the following exercises, evaluate the expressions, writing the result as a simplified complex number. 3 + 2i 2+i + (4 + 3i)
For the following exercises, write an equation for a rational function with the given characteristics.Vertical asymptote at x = −1, double zero at x = 2, y-intercept at (0, 2)
For the following exercises, find the inverse of the functions with a, b, c positive real numbers. f(x) = = ax + b x + c
For the following exercises, use the graph to identify zeros and multiplicity. y Diện
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
For the following exercises, graph the polynomial functions using a calculator. Based on the graph, determine the intercepts and the end behavior.f(x) = x3 − 27
For the following exercises, use the given information to answer the questions.The intensity of light measured in foot-candles varies inversely with the square of the distance from the light source.
For the following exercises, use a calculator with CAS to answer the questions. with k = 1, 2, 3. What do you expect Consider x + 1 the result to be if k= 4?
For the following exercises, write an equation for a rational function with the given characteristics.Vertical asymptote at x = 3, double zero at x = 1, y-intercept at (0, 4)
For the following exercises, evaluate the expressions, writing the result as a simplified complex number. 4+i + 3 - 4i 1-i
For the following exercises, list all possible rational zeros for the functions.f(x) = x4 + 3x3 − 4x + 4
For the following exercises, use the given information about the polynomial graph to write the equation.Degree 3. Zeros at x = −2, x = 1, and x = 3. y-intercept at (0, −4).
For the following exercises, sketch a graph of the quadratic function and give the vertex, axis of symmetry, and intercepts.f(x) = −2x2 + 5x − 8
For the following exercises, graph the polynomial functions using a calculator. Based on the graph, determine the intercepts and the end behavior.f(x) = x4 − 81
For the following exercises, use the graphs to write an equation for the function. T H -10-8-6-4-20 2 4 6 8 10 234 # -5- X
For the following exercises, use the given information to answer the questions.The current in a circuit varies inversely with its resistance measured in ohms. When the current in a circuit is 40
For the following exercises, evaluate the expressions, writing the result as a simplified complex number. 3 + 21 1 + 2i 2 - 3i 3+i
For the following exercises, list all possible rational zeros for the functions.f(x) = 2x3 + 3x2 − 8x + 5
For the following exercises, use the given information about the polynomial graph to write the equation.Degree 3. Zeros at x = −5, x = −2, and x = 1. y-intercept at (0, 6)
For the following exercises, sketch a graph of the quadratic function and give the vertex, axis of symmetry, and intercepts.f(x) = 4x2 − 12x − 3
For the following exercises, determine the function described and then use it to answer the question.An object dropped from a height of 600 feet has a height, h(t), in feet after t seconds have
For the following exercises, graph the polynomial functions using a calculator. Based on the graph, determine the intercepts and the end behavior.f(x) = −x3 + x2 + 2x
For the following exercises, solve the equations over the complex numbers.5x2 − 8x + 5 = 0
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
For the following exercises, graph the polynomial functions. Note x- and y-intercepts, multiplicity, and end behavior.n(x) = −3x(x + 2)(x − 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
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
For the following exercises, use the graphs to write the formula for a polynomial function of least degree. I 4-3 f(x) 1200 HE ★x
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
For the following exercises, evaluate the expressions, writing the result as a simplified complex number. 1 4
For the following exercises, find the unknown value.y varies directly as the square of x. If when x = 3,y = 36, find y if x = 4.
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 + 3x − 4, y = 0, 1, 2
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, 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) = (−5, 3), (x, y) = (2, 9)
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
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
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
For the following exercises, use synthetic division to find the quotient and remainder. 4x³ - 33 x-2
For the following exercises, use the graphs to write the formula for a polynomial function of least degree. man "D" f(x) jende
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 + 8x − 4, y = −1, 0, 1
For the following exercises, make a table to confirm the end behavior of the function. x5 .f(x) = - x² 10
For the following exercises, find the unknown value.y varies inversely as the square root of x. If when x = 25, y = 2, find y if x = 4.
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) = (3, 2), (x, y) = (10, 1)
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
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
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
For the following exercises, use synthetic division to find the quotient and remainder. 2x³ +25 x + 3
For the following exercises, use the graphs to write the formula for a polynomial function of least degree. 1-4-3-2 f(x) 14.0 2014 fre x+
For the following exercises, use the graphs to write the formula for a polynomial function of least degree. f(x) I x II Amam
For the following exercises, evaluate the expressions, writing the result as a simplified complex number. i'(1 + i²)
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) = x4 + 5x + 1, y = −1, 0, 1
For the following exercises, find the unknown value.y varies jointly as the cube of x and as z. If when x = 1 and z = 2, y = 6, find y if x = 2 and z = 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) = (1, 0)
For the following exercises, graph the polynomial functions using a calculator. Based on the graph, determine the intercepts and the end behavior.f(x) = x3 (x − 2)
For the following exercises, use the given information to answer the questions.The distance s that an object falls varies directly with the square of the time, t, of the fall. If an object falls 16
For the following exercises, write an equation for a rational function with the given characteristics.Vertical asymptotes at x = 5 and x = −5, x-intercepts at (2, 0) and (−1, 0), y-intercept at
For the following exercises, use synthetic division to find the quotient and remainder. 3x³ + 2x - 5 x-1
For the following exercises, use the graphs to write the formula for a polynomial function of least degree. 5-2 I f(x) A
For the following exercises, evaluate the expressions, writing the result as a simplified complex number. -3 i³ + 51²
For the following exercises, find the inverse of the functions with a, b, c positive real numbers.f(x) = ax3 + b
For the following exercises, find the unknown value.y varies jointly as x and the square of z and inversely as the cube of w. If when x = 3, z = 4, and w = 2, y = 48, find y if x = 4, z = 5, and w =
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) = (1, 0), (x, y) = (0, 1)
For the following exercises, graph the polynomial functions using a calculator. Based on the graph, determine the intercepts and the end behavior.f(x) = x(x − 3)(x + 3)
For the following exercises, use the given information to answer the questions.The velocity v of a falling object varies directly to the time, t, of the fall. If after 2 seconds, the velocity of the
For the following exercises, write an equation for a rational function with the given characteristics.Vertical asymptotes at x = −4 and x = −1, x-intercepts at (1, 0) and (5, 0), y-intercept at
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
For the following exercises, use synthetic division to find the quotient and remainder. -4x²-x²-12 x+4
For the following exercises, use the graph to identify zeros and multiplicity. 11 y **** fugl
For the following exercises, evaluate the expressions, writing the result as a simplified complex number. (2+ i)(4-21) (1 + i)
For the following exercises, find the inverse of the functions with a, b, c positive real numbers.f(x) = x2 + bx
For the following exercises, use synthetic division to find the quotient.(x4 + 2x3 − 3x2 + 2x + 6) ÷ (x + 3)
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, 4x3 − 3x2 − 8x + 4
For the following exercises, perform the indicated operation and express the result as a simplified complex number. -V-4-4V-25
For the following rational functions, find the intercepts and the vertical and horizontal asymptotes, and then use them to sketch a graph. f(x) = 3x² - 27 x²2²+x-2
For the following exercises, find the zeros and give the multiplicity of each.f(x) = 3x4 + 6x3 + 3x2
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
For the following exercises, find the inverse of the function and graph both the function and its inverse.f(x) = x2 − 6x + 1, x ≥ 3
For the following exercises, solve the equations over the complex numbers.2x2 + 2x + 5 = 0
For the following exercises, use the given information to find the unknown value.y varies jointly as the square of x and the cube of z and inversely as the square root of w. When x = 2, z = 2, and w
For the following exercises, use the Rational Zero Theorem to find all real zeros.8x4 + 26x3 + 39x2 + 26x + 6
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, 3x4 − 6x3 − 5x + 10
For the following exercises, perform the indicated operation and express the result as a simplified complex number. 2+ V-12 2
For the following exercises, find the zeros and give the multiplicity of each.f(x) = 4x5 − 12x4 + 9x3
For the following rational functions, find the intercepts and the vertical and horizontal asymptotes, and then use them to sketch a graph. f(x) = x + 2 x²-9
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
For the following exercises, use a calculator to graph the equation implied by the given variation.y varies directly with the square of x and when x = 2, y = 3.
For the following exercises, find the inverse of the function and graph both the function and its inverse. 0 = x < ²² = (x) f I

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