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mathematics
precalculus 1st
Precalculus 1st Edition Jay Abramson - Solutions
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 = −2.
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 = 36, then y = 48.
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 = 3, z = 4, and w = 3, then y = 6.
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 helium reserves, R, in terms of t, the number of years since 2010.b. In 2015, what will the helium
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
For the following exercises, find the x- or t-intercepts of the polynomial functions.f(x) = x3 + 2x2 − 9x − 18
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