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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

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.
For the following exercises, use the Rational Zero Theorem to find all real zeros.3x3 − x2 − 11x − 6 = 0
For the following exercises, use synthetic division to find the quotient.(x4 − 3x2 + 1) ÷ (x − 1)
For the following exercises, find the zeros and give the multiplicity of each.f(x) = (x + 2)3 (x − 3)2
For the following exercises, perform the indicated operation and express the result as a simplified complex number.3 + 4i/2
For the following exercises, find the slant asymptote of the functions. f(x) = 4x²2 - 10 2x - 4
For the following exercises, solve the equations over the complex numbers.x2 − 4x + 5 = 0
For the following exercises, use the given information to find the unknown value.y varies inversely with the cube of x. When x = 3, then y = 1. Find y when x = 1.
For the following exercises, determine the least possible degree of the polynomial function shown. y الا بنا 2 3 4 5 X
For the following exercises, use the Rational Zero Theorem to find all real zeros.2x3 − 5x2 + 9x − 9 = 0
For the following exercises, find the slant asymptote of the functions. f(x) = = 81x² 18 - 3x - 2
For the following exercises, find the zeros and give the multiplicity of each.f(x) = x2 (2x + 3)5 (x − 4)2
For the following exercises, perform the indicated operation and express the result as a simplified complex number.6 − 2i/3
For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation.2x3 − 3x2 − 18x − 8 = 0
For the following exercises, find the inverse of the function and graph both the function and its inverse.f(x) = x2 + 2, x ≥ 0
For the following exercises, determine the least possible degree of the polynomial function shown. 30 y -5-4-3 ·3+ 2- IN x
For the following exercises, solve the equations over the complex numbers.x2 + 8x + 25 = 0
For the following exercises, use the given information to find the unknown value.y varies inversely with the square root of x. When x = 64, then y = 12. Find y when x = 36.
For the following exercises, use the Rational Zero Theorem to find all real zeros.2x3 − 3x2 + 4x + 3 = 0
For the following exercises, find the slant asymptote of the functions. f(x) = 6x³ - 5x 3x² + 4
For the following exercises, use synthetic division to find the quotient.(x4 − 10x3 + 37x2 − 60x + 36) ÷ (x − 2)
For the following exercises, find the zeros and give the multiplicity of each.f(x) = x3 (x − 1)3 (x + 2)
For the following exercises, perform the indicated operation and express the result as a simplified complex number.−5 + 3i/2i
For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation.3x3 + 11x2 + 8x − 4 = 0
For the following exercises, find the inverse of the function and graph both the function and its inverse.f(x) = 4 − x2 , x ≥ 0
For the following exercises, solve the equations over the complex numbers.x2 − 4x + 13 = 0
For the following exercises, use the given information to find the unknown value.y varies inversely with the cube root of x. When x = 27, then y = 5. Find y when x = 125.
For the following exercises, use the Rational Zero Theorem to find all real zeros.x4 − 2x3 − 7x2 + 8x + 12 = 0
For the following exercises, determine the least possible degree of the polynomial function shown. HI 5-4-3 y -5- -4 -3- 45 # X
For the following exercises, use synthetic division to find the quotient.(x4 − 8x3 + 24x2 − 32x + 16) ÷ (x − 2)
For the following exercises, find the zeros and give the multiplicity of each.f(x) = x2 (x2 + 4x + 4)
For the following exercises, perform the indicated operation and express the result as a simplified complex number.6 + 4i/i
For the following exercises, find the slant asymptote of the functions. f(x) = x² + 5x + 4 x-1
For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation.2x4 − 17x3 + 46x2 − 43x + 12 = 0
For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation.4x4 + 8x3 + 19x2 + 32x + 12 = 0
For the following exercises, find the inverse of the function and graph both the function and its inverse.f(x) = (x + 3)2 , x ≥ −3
For the following exercises, solve the equations over the complex numbers.x2 + 6x + 25 = 0
For the following exercises, use the given information to find the unknown value.y varies jointly as x and z. When x = 4 and z = 2, then y = 16. Find y when x = 3 and z = 3.
For the following exercises, use the Rational Zero Theorem to find all real zeros.x4 + 2x3 − 9x2 − 2x + 8 = 0
For the following exercises, use synthetic division to find the quotient.(x4 + 5x3 − 3x2 − 13x + 10) ÷ (x + 5)
For the following exercises, find the zeros and give the multiplicity of each.f(x) = (2x + 1)3 (9x2 − 6x + 1)
For the following exercises, perform the indicated operation and express the result as a simplified complex number.2 − 3i/4 + 3i
For the following exercises, use Descartes’ Rule of Signs to find the possible number of positive and negative solutions.x3 − 3x2 − 2x + 4 = 0
For the following exercises, determine the least possible degree of the polynomial function shown. y 54 4+ -5- 2 3 4 5 100 X
For the following exercises, find the inverse of the function and graph both the function and its inverse.f(x) = (x − 4)2 , x ≥ 4
For the following exercises, solve the equations over the complex numbers.x2 − 10x + 26 = 0
For the following exercises, use the given information to find the unknown value.y varies jointly as x, z, and w. When x = 2, z = 1, and w = 12, then y = 72. Find y when x = 1, z = 2, and w = 3.
For the following exercises, use the given transformation to graph the function. Note the vertical and horizontal asymptotes.The reciprocal function shifted up two units.
For the following exercises, use the Rational Zero Theorem to find all real zeros.4x4 + 4x3 − 25x2 − x + 6 = 0
For the following exercises, use synthetic division to find the quotient.(x4 − 12x3 + 54x2 − 108x + 81) ÷ (x − 3)
For the following exercises, find the zeros and give the multiplicity of each.f(x) = (3x + 2)5 (x2 − 10x + 25)
For the following exercises, perform the indicated operation and express the result as a simplified complex number.3 + 4i/2 − i
For the following exercises, determine the least possible degree of the polynomial function shown. -5-4-3-2-1 y -2- TI 2 3 4 5 III x
For the following exercises, use Descartes’ Rule of Signs to find the possible number of positive and negative solutions.2x4 − x3 + 4x2 − 5x + 1 = 0
For the following exercises, find the inverse of the function and graph both the function and its inverse.f(x) = x3 + 3
For the following exercises, solve the equations over the complex numbers.x2 − 6x + 10 = 0
For the following exercises, use the given information to find the unknown value.y varies jointly as x and the square of z. When x = 2 and z = 4, then y = 144. Find y when x = 4 and z = 5.
For the following exercises, use the given transformation to graph the function. Note the vertical and horizontal asymptotes.The reciprocal function shifted down one unit and left three units.
For the following exercises, use the Rational Zero Theorem to find all real zeros.2x4 − 3x3 − 15x2 + 32x − 12 = 0
For the following exercises, use synthetic division to find the quotient.(4x4 − 2x3 − 4x + 2) ÷ (2x − 1)
For the following exercises, find the zeros and give the multiplicity of each.f(x) = x(4x2 − 12x + 9)(x2 + 8x + 16)
For the following exercises, perform the indicated operation and express the result as a simplified complex number.2 + 3i/2 − 3i
For the following rational functions, find the intercepts and the vertical and horizontal asymptotes, and then use them to sketch a graph. GN f(x)= x+2 x-5
For the following exercises, determine the least possible degree of the polynomial function shown. E y o a I N V 1 2 3 4 5 X
For the following exercises, find the inverse of the function and graph both the function and its inverse.f(x) = 1 − x3
For the following exercises, solve the equations over the complex numbers.x(x − 4) = 20
For the following exercises, perform the indicated operation and express the result as a simplified complex number. V-9 + 3 V-16
For the following exercises, use the given information to find the unknown value.y varies jointly as the square of x and the square root of z. When x = 2 and z = 9, then y = 24. Find y when x = 3 and
For the following rational functions, find the intercepts and the vertical and horizontal asymptotes, and then use them to sketch a graph. f(x) = x² +1 x² - 4
For the following exercises, use the given transformation to graph the function. Note the vertical and horizontal asymptotes.The reciprocal squared function shifted to the right 2 units.
For the following exercises, use the Rational Zero Theorem to find all real zeros.x4 + 2x3 − 4x2 − 10x − 5 = 0
For the following exercises, use synthetic division to find the quotient.(4x4 + 2x3 − 4x2 + 2x + 2) ÷ (2x + 1)
For the following exercises, determine the least possible degree of the polynomial function shown. ILLO HI y 1 2 3 4 5 III -X
For the following exercises, find the zeros and give the multiplicity of each.f(x) = x6 − x5 − 2x4
For the following exercises, find the inverse of the function and graph both the function and its inverse.f(x) = x2 + 4x, x ≥ −2
For the following exercises, solve the equations over the complex numbers.x(x − 2) = 10
For the following exercises, use the given information to find the unknown value.y varies jointly as x and z and inversely as w. When x = 5, z = 2, and w = 20, then y = 4. Find y when x = 3 and z =
For the following exercises, use the given transformation to graph the function. Note the vertical and horizontal asymptotes.The reciprocal squared function shifted down 2 units and right 1 unit.
For the following exercises, use the Rational Zero Theorem to find all real zeros.4x3 − 3x + 1 = 0
For the following exercises, based on the given graph, determine the zeros of the function and note multiplicity. y 30 பிற்பட -10-8-6-4-2 -10- II FEE 6 8 10 x
For the following exercises, find the inverse of the functions. f(x): || 3 x-4
For the following exercises, perform the indicated operation and express the result as a simplified complex number.(5 − 2i)(3i)
For the following exercises, determine the end behavior of the functions.f(x) = (2 − x)7
For the following exercises, use the given information to find the unknown value.y varies directly as x. When x = 3, then y = 12. Find y when x = 20.
For the following exercises, use the Rational Zero Theorem to find all real zeros.x3 + 2x2 − 9x − 18 = 0
For the following exercises, find the inverse of the functions. f(x) = x+3 x+7
For the following exercises, perform the indicated operation and express the result as a simplified complex number.(6 − 2i)(5)
Use the Intermediate Value Theorem to show that at least one zero lies between 2 and 3 for the function.f(x) = x3 − 5x + 1
For the following exercises, describe the local and end behavior of the functions. f(x) = X 2x + 1
For the following exercises, determine the domain and range of the quadratic function.k(x) = 3x2 − 6x − 9
For the following exercises, use the Rational Zero Theorem to find all real zeros.x3 + 5x2 − 16x − 80 = 0
For the following exercises, use synthetic division to find the quotient.(x3 − 21x2 + 147x − 343) ÷ (x − 7)
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 − 9x, between x = 2 and x = 4.
For the following exercises, use long division to find the quotient and remainder. x³ 2x² + 4x + 4 x-2
For the following exercises, find the inverse of the functions. f(x) = x-2 x + 7
For the following exercises, find the intercepts of the functions.g(n) = −2(3n − 1)(2n + 1)
For the following exercises, use the given information to find the unknown value.y varies directly as the cube of x. When x = 3, then y = 5. Find y when x = 4.
For the following exercises, solve the equations over the complex numbers. x2 = −25
For the following exercises, find the x- and y-intercepts for the functions. f(x) = 94 - 2x² 12 3x²
For the following exercises, determine the domain and range of the quadratic function.f(x) = 2x2 − 4x + 2

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