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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

For the following exercises, use synthetic division to find the quotient.(x3 − 3x + 2) ÷ (x + 2)
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 = −4 and x =
For the following exercises, find the intercepts of the functions.f(t) = 2(t − 1)(t + 2)(t − 3)
For the following exercises, use the given information to find the unknown value.y varies directly as the square of x. When x = 2, then y = 16. Find y when x = 8.
For the following exercises, describe the local and end behavior of the functions. f(x)= = 2x x-6
For the following exercises, perform the indicated operation and express the result as a simplified complex number.(−2 + 4i)(8)
For the following exercises, use long division to find the quotient and remainder. 3x² - 4x² + 4x + 8 x+1
For the following exercises, find the inverse of the functions. f(x)= 3x + 4 5 - 4x
For the following exercises, describe the local and end behavior of the functions. f(x): -2x x-6
For the following exercises, use the Rational Zero Theorem to find all real zeros.x3 − 3x2 − 25x + 75 = 0
For the following exercises, use synthetic division to find the quotient.(x3 − 15x2 + 75x − 125) ÷ (x − 5)
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) = x5 − 2x, between x = 1 and x = 2.
For the following exercises, perform the indicated operation and express the result as a simplified complex number.(2 + 3i)(4 − i)
For the following exercises, find the intercepts of the functions.f(x) = x4 − 16
For the following exercises, use synthetic division to find the quotient. If the divisor is a factor, then write the factored form. x³ 2x² + 5x - 1 x + 3
For the following exercises, use the given information to find the unknown value.y varies directly as the square root of x. When x = 16, then y = 4. Find y when x = 36.
For the following exercises, find the inverse of the functions. f(x)= || 5x + 1 2 - 5x
For the following exercises, solve the equations over the complex numbers.x2 = −8
For the following exercises, use the Rational Zero Theorem to find all real zeros.2x3 − 3x2 − 32x − 15 = 0
For the following exercises, use synthetic division to find the quotient.(9x3 − x + 2) ÷ (3x − 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) = −x4 + 4, between x = 1 and x = 3.
For the following exercises, perform the indicated operation and express the result as a simplified complex number.(−1 + 2i)(−2 + 3i)
For the following exercises, describe the local and end behavior of the functions. f(x)= x² - 4x + 3 x² - 4x - 5
For the following exercises, find the intercepts of the functions.f(x) = x3 + 27
For the following exercises, solve the equations over the complex numbers.x2 + 36 = 0
For the following exercises, use the given information to find the unknown value.y varies directly as the cube root of x. When x = 125, then y = 15. Find y when x = 1,000.
For the following exercises, use the Rational Zero Theorem to find all real zeros.2x3 + x2 − 7x − 6 = 0
For the following exercises, use synthetic division to find the quotient.(6x3 − x2 + 5x + 2) ÷ (3x + 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) = −2x3 − x, between x = −1 and x = 1.
Describe a use for the Remainder Theorem.
For the following exercises, determine end behavior of the polynomial function. f(x) = 4x³6x² +2
For the following exercises, use synthetic division to find the quotient.(9x3 − 9x2 + 18x + 5) ÷ (3x − 1)
For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. f(x) = 4 - 2x 3x-1
For the following exercises, find the x- or t-intercepts of the polynomial functions.f(x) = x6 − 7x3 − 8
For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry.f(x) = 1/2 x2 + 3x + 1
For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor.x3 + 3x2 + 4x + 12; x + 3
For the following exercises, use synthetic division to find the quotient.(3x3 − 2x2 + x − 4) ÷ (x + 3)
For the following exercises, find the x- or t-intercepts of the polynomial functions.f(x) = 2x4 + 6x2 − 8
For the following exercises, find all zeros of the polynomial function, noting multiplicities. f(x) = (x + 3)²(2x − 1)(x + 1)³ -
For the following exercises, find the inverse of the functions. f(x) = √6x-8 +5
For the following exercises, perform the indicated operation and express the result as a simplified complex number.(−5 + 3i) − (6 − i)
For the following exercises, determine the end behavior of the functions. f(x) = −x9
For the following exercises, write an equation describing the relationship of the given variables.y varies jointly as the square of x the cube of z and the square root of w. When x = 1, z = 2, and w
For the following exercises, find the x- and y-intercepts for the functions. f(x) = x+5 x² + 4
For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry.f(x) = −1/3 x2 − 2x + 3
For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor.4x3 − 7x + 3; x − 1
For the following exercises, use synthetic division to find the quotient.(−6x3 + x2 − 4) ÷ (2x − 3)
For the following exercises, find the x- or t-intercepts of the polynomial functions.f(x) = x3 − 3x2 − x + 3
For the following exercises, find all zeros of the polynomial function, noting multiplicities. f(x)=x² + 4x + 4x³
For the following exercises, perform the indicated operation and express the result as a simplified complex number.(2 − 3i) − (3 + 2i)
For the following exercises, find the inverse of the functions. f(x) = 9+2√x
For the following exercises, find the x- and y-intercepts for the functions. f(x) = X ४ x²-x
For the following exercises, determine the end behavior of the functions. f(x) = −2x4 − 3x2 + x − 1
For the following exercises, write an equation describing the relationship of the given variables.y varies jointly as x and z and inversely as w. When x = 3, z = 5, and w = 6, then y = 10.
For the following exercises, determine the domain and range of the quadratic function. f(x) = (x − 3)2 + 2
For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor.2x3 + 5x2 − 12x − 30, 2x + 5
For the following exercises, find all zeros of the polynomial function, noting multiplicities. f(x) = x³ − 4x² + x - 4
For the following exercises, use synthetic division to find the quotient.(2x3 + 7x2 − 13x − 3) ÷ (2x − 3)
For the following exercises, find the x- or t-intercepts of the polynomial functions.f(x) = x6 − 2x4 − 3x2
For the following exercises, find the inverse of the functions. f(x)=3-√x
For the following exercises, perform the indicated operation and express the result as a simplified complex number.(−4 + 4i) − (−6 + 9i)
For the following exercises, find the x- and y-intercepts for the functions. f(x): = x² + 8x + 7 x² + 11x + 30
For the following exercises, determine the end behavior of the functions. f(x) = 3x2 + x − 2
For the following exercises, write an equation describing the relationship of the given variables.y varies jointly as the square of x and the square root of z and inversely as the cube of w. When x =
For the following exercises, determine the domain and range of the quadratic function.f(x) = −2(x + 3)2 − 6
For the following exercises, based on the given graph, determine the zeros of the function and note multiplicity. 201 16+ 3:2+ FFF m Xx
For the following exercises, use the Rational Zero Theorem to find all real zeros.x3 − 3x2 − 10x + 24 = 0
For the following exercises, find the inverse of the functions. f(x) = 2 x+8
For the following exercises, use synthetic division to find the quotient.(3x3 − 5x2 + 2x + 3) ÷ (x + 2)
For the following exercises, find the x- or t-intercepts of the polynomial functions.f(x) = x6 − 3x4 − 4x2
For the following exercises, perform the indicated operation and express the result as a simplified complex number.(2 + 3i)(4i)
For the following exercises, find the x- and y-intercepts for the functions. f(x) = x²+x+6 x²10x + 24
For the following exercises, determine the end behavior of the functions.f(x) = x2 (2x3 − x + 1)
For the following exercises, determine the domain and range of the quadratic function.f(x) = x2 + 6x + 4
For the following exercises, use the Rational Zero Theorem to find all real zeros.2x3 + 7x2 − 10x − 24 = 0
For the following exercises, use synthetic division to find the quotient.(4x3 − 5x2 + 13) ÷ (x + 4)
For the following exercises, find the x- or t-intercepts of the polynomial functions.f(x) = x5 − 5x3 + 4x
The Federal Helium Reserve held about 16 billion cubic feet of helium in 2010 and is being depleted by about 2.1 billion cubic feet each year.a. Give a linear equation for the remaining federal
For the following exercises, determine if the function is a polynomial function and, if so, give the degree and leading coefficient. +1 f(x) = 5x+¹-x²
For the following exercises, sketch the graph of each equation.r(x) = 4
For the following exercises, find the x- or t-intercepts of the polynomial functions.f(x) = x3 + 6x2 − 7x
For the following exercises, plot the complex numbers on the complex plane.−2 + 3i
For the following exercises, find the inverse of the functions. f(x) = 3x3 + 1
For the following exercises, find the degree and leading coefficient for the given polynomial.x(4 − x2 )(2x + 1)
For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. f(x) = 3x - 4 x³ 16x
For the following exercises, write an equation describing the relationship of the given variables.y varies inversely as the cube root of x and when x = 64, y = 5.
For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry.f(x) = 2x2 − 10x + 4
For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor.f(x) = 2x3 + x2 − 5x + 2; x + 2
For the following exercises, determine if the function is a polynomial function and, if so, give the degree and leading coefficient. f(x) = x²(3-6x + x²)
For the following exercises, use synthetic division to find the quotient.(2x3 − 6x2 − 7x + 6) ÷ (x − 4)
For the following exercises, find the x- or t-intercepts of the polynomial functions.f(x) = x3 + x2 − 4x − 4
For the following exercises, find the inverse of the functions. f(x) = 4 − x3
For the following exercises, find the inverse of the functions. f(x) = 4 − 2x3
For the following exercises, find the degree and leading coefficient for the given polynomial.x2 (2x − 3)2
For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. f(x) = x² - 1 x³ + 9x² + 14x
For the following exercises, write an equation describing the relationship of the given variables.y varies jointly with x and z and when x = 2 and z = 3, y = 36.
For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry.f(x) = −x2 + 4x + 3
For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor.f(x) = 3x3 + x2 − 20x + 12; x + 3
For the following exercises, use synthetic division to find the quotient.(6x3 − 10x2 − 7x − 15) ÷ (x + 1)
For the following exercises, determine end behavior of the polynomial function. f(x) = 2x² + 3x³ - 5x² +7

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