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mathematics
precalculus

Questions and Answers of Precalculus

Is the set of ordered pairs 1(1, 3), (2, 3), (-1, 2)) a function? Why or why not?
A strain of E-coli Beu 397-recA441 is placed into a nutrient broth at 30° Celsius and allowed to grow. The following data are collected. Theory states that the number of bacteria in the petri dish
The size P of a certain insect population at time t (in days) obeys the functionP(t) = 500e0.02t.(a) Determine the number of insects at t = 0 days.(b) What is the growth rate of the insect
Solve each inequality:(a) 3x - 7 ≤ 8 - 2x(b) x2 - x - 6 > 0
Solve x2 - 7x - 30 = 0.
Solve: 43 = _____ ;82/3 = __________; 3-2 = ________.
What is the interest due if $500 is borrowed for 6 months at a simple interest rate of 6% per annum?
In problem, find an equation of the line L.L is perpendicular to y = 2x Ул (1, 2) -1 У - 2xF 3х
In problem, determine whether each relation represents a function. For each function, state the domain and range.{(-4, 4), (-3, 3), (-2, 2), (3, 3)}
In problem, determine whether each relation represents a function. For each function, state the domain and range.{(-2, 4), (-2, 6), (0, 3), (3, 7)}
In problem, determine whether each relation represents a function. For each function, state the domain and range.{(2, 6), (-3, 6), (4, 9), (2, 10)}
In problem, determine whether each relation represents a function. For each function, state the domain and range. Hours Worked Salary 20 Hours $200 $300 30 Hours $350 40 Hours $425
In problem, determine whether each relation represents a function. For each function, state the domain and range. Father Daughter Bob Beth Diane John Linda Marcia Chuck
A function is defined byf(x) = Ax + 5/6x - 2If f(1) = 4, find A.
A function g is defined byf(x) = A/x + 8/x2If g(-1) = 0, find A.
Given f(x) = 3x + 1 and (f + g)(x) = 6 – 1/2x, find the function g.
Given f(x) = 1/x andfind the function g. x + 1 )(x)
In problem, find the difference quotient of f; that is, find f(x + h) - f(x)/h for each function. Be sure to simplify.f(x) = 4x + 3
In problem, find the difference quotient of f; that is, find f(x + h) - f(x)/h for each function. Be sure to simplify.f(x) -3x + 1
In problem, find the difference quotient of f; that is, find f(x + h) - f(x)/h for each function. Be sure to simplify.f(x) = x2 - x + 4
In problem, find the difference quotient of f; that is, find f(x + h) - f(x)/h for each function. Be sure to simplify.f(x) = 3x2 - 2x + 6
In problem, find the difference quotient of f; that is, find f(x + h) - f(x)/h for each function. Be sure to simplify.f(x) = 1/x2
In problem, find the difference quotient of f; that is, find f(x + h) - f(x)/h for each function. Be sure to simplify.f(x) = √x
In problem, find the difference quotient of f; that is, find f(x + h) - f(x)/h for each function. Be sure to simplify.f(x) = √x + 1
If f(x) = 2x3 + Ax2 + 4x -5 and f(2) = 5, what is the value of A?
In problem, analyze each polynomial function f by following Steps 1 through 8.f(x) = x3 + 2.56x2 - 3.31x + 0.89
In problem, each polynomial function has exactly one positive zero. Use the method of Example 9 to approximate the zero correct to two decimal places.f(x) = 2x4 - 3x3 - 4x2 - 8
In problem, graph each polynomial function.f(x) = 2x3 - x2 + 2x - 1
In problem, analyze each polynomial function f by following Steps 1 through 8.f(x) = -1.2x4 + 0.5x2 – √3x + 2
Can the graph of a polynomial function have no y-intercept? Can it have no x-intercepts? Explain.
In problem, graph each polynomial function.f(x) = 4x5 + 12x4 - x - 3
In problem, construct a polynomial function f with the given characteristics.Zeros: -3, 1, 4; degree 3; y-intercept: 36
Find k such that f(x) = x3 - kx2 + kx + 2 has the factor x – 2.
In problem, construct a polynomial function f with the given characteristics.Zeros: -4, -1, 2; degree 3; y-intercept: 16
Find k such that f(x) = x4 - kx3 + kx2 + 1 has the factor x + 2.
In problem, construct a polynomial function f with the given characteristics.Zeros: -5 (multiplicity 2); 2 (multiplicity 1); 4 (multiplicity 1); degree 4; contains the point (3, 128)
What is the remainder when f(x) = 2x20 - 8x10 + x – 2 is divided by x - 1?
In problem, construct a polynomial function f with the given characteristics.Zeros: -4 (multiplicity 1); 0 (multiplicity 3); 2 (multiplicity 1); degree 5; contains the point (-2, 64)
What is the remainder when f(x) = - 3x17 + x9 - x5 + 2x is divided by x + 1?
G(x) = (x + 3)2(x - 2)(a) Identify the x-intercepts of the graph of G.(b) What are the x-intercepts of the graph of y = G(x + 3)?
Use the Factor Theorem to prove that x – c is a factor of xn – cn for any positive integer n.
h(x) = (x + 2)(x - 4)3(a) Identify the x-intercepts of the graph of h.(b) What are the x-intercepts of the graph of y = h(x - 2)?
Use the Factor Theorem to prove that x + c is a factor of xn + cn if n ≥ 1is an odd integer.
In 2005, Hurricane Katrina struck the Gulf Coast of the United States, killing 1289 people and causing an estimated $200 billion in damage. The following data represent the number of major hurricane
One solution of the equation x3 - 8x2 + 16x - 3 = 0 is 3. Find the sum of the remaining solutions.
One solution of the equation x3 + 5x2 + 5x - 2 = 0 is -2. Find the sum of the remaining solutions.
The following data represent the cost C (in thousands of dollars) of manufacturing Chevy Cobalts and the number x of Cobalts produced.(a) Draw a scatter diagram of the data using x as the independent
What is the length of the edge of a cube if, after a slice 1 inch thick is cut from one side, the volume remaining is 294 cubic inches?
The following data represent the temperature T ( Fahrenheit) in Kansas City, Missouri, x hours after midnight on May 15, 2010.Hours after Midnight, x ……………………….. Temperature (°F),
What is the length of the edge of a cube if its volume could be doubled by an increase of 6 centimeters in one edge, an increase of 12 centimeters in a second edge, and a decrease of 4 centimeters in
Suppose that you make deposits of $500 at the beginning of every year into an Individual Retirement Account (IRA) earning interest r. At the beginning of the first year, the value of the account will
Let f(x) be a polynomial function whose coefficients are integers. Suppose that r is a real zero of f and that the leading coefficient of f is 1. Use the Rational Zeros Theorem to show that r is
In calculus, you will learn that certain functions can be approximated by polynomial functions. We will explore one such function now.(a) Using a graphing utility, create a table of values withY1 =
Prove the Rational Zeros Theorem.Let p/q, where p and q have no common factors except 1 and -1, be a zero of the polynomial function whose coefficients are all integers. Show thatNow, because p
We begin with two consecutive integers, a and a + 1, such that f(a) and f(a - 1) are of opposite sign. Evaluate f at the midpoint m1 of a and a + 1. If f(m1) = 0, then m1 is the zero of f and we are
Is 1/3 a zero of f(x) = 2x3 + 3x2 - 6x + 7? Explain.
Make up a polynomial that has the following characteristics: crosses the x-axis -1 at and 4, touches the x-axis at 0 and 2, and is above the x-axis between 0 and 2. Give your polynomial to a fellow
Is 1/3 a zero of f(x) = 4x3 - 5x2 - 3x + 1? Explain.
Make up two polynomials, not of the same degree, with the following characteristics: crosses the x-axis at -2, touches the x-axis at 1, and is above the x-axis between -2 and 1. Give your polynomials
Is 3/5 a zero of f(x) = 2x6 - 5x4 + x3 - x + 1? Explain.
The graph of a polynomial function is always smooth and continuous. Name a function studied earlier that is smooth and not continuous. Name one that is continuous, but not smooth.
Is a zero of f(x) = x7 + 6x5 – x4 + x + 2? Explain.
Which of the following statements are true regarding the graph of the cubic polynomial f(x) = x3 + bx2 + cx + d? (Give reasons for your conclusions.)(a) It intersects the y-axis in one and only
The illustration shows the graph of a polynomial function.(a) Is the degree of the polynomial even or odd?(b) Is the leading coefficient positive or negative?(c) Is the function even, odd, or
Design a polynomial function with the following characteristics: degree 6; four distinct real zeros, one of multiplicity 3; y-intercept 3; behaves like y = -5x6 for large values of |x|. Is this
In problem, each equation has a solution r in the interval indicated. Use the method of Example 9 to approximate this solution correct to two decimal places.x4 + 8x3 – x2 + 2 = 0; -1 ≤ r ≤ 0
In problem, each equation has a solution r in the interval indicated. Use the method of Example 9 to approximate this solution correct to two decimal places.2x3 + 6x2 - 8x + 2 = 0; -5 ≤ r ≤ -4
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = x2 (x - 2)(x2 + 3)
In problem, find the complex zeros of each polynomial function f(x).Write f in factored form.f(x) = 2x4 + 2x3 - 11x2 + x – 6
In problem, each equation has a solution r in the interval indicated. Use the method of Example 9 to approximate this solution correct to two decimal places.3x3 - 10x + 9 = 0; -3 ≤ r ≤ -2
In problem, find the complex zeros of each polynomial function f(x).Write f in factored form.f(x) = 3x4 + 3x3 - 17x2 + x - 6
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = x2 (x2 + 1)(x + 4)
In problem, analyze each polynomial function f by following Steps 1 through 8.f(x) = x3 + 0.2x2 - 1.5876x - 0.31752
A can in the shape of a right circular cylinder is required to have a volume of 250 cubic centimeters.(a) Express the amount A of material to make the can as a function of the radius r of the
In problem, each polynomial function has exactly one positive zero. Use the method of Example 9 to approximate the zero correct to two decimal places.f(x) = x3 + x2 + x - 4
In problem, analyze each polynomial function f by following Steps 1 through 8.f(x) = x3 - 0.8x2 - 4.6656x + 3.73248
In problem, each polynomial function has exactly one positive zero. Use the method of Example 9 to approximate the zero correct to two decimal places.f(x) = 2x4 + x2 - 1
The following data represent the percentage of families in the United States whose income is below the poverty level.
In problem, analyze each polynomial function f by following Steps 1 through 8.f(x) = x3 - 2.91x2 - 7.668x - 3.8151
In problem, each polynomial function has exactly one positive zero. Use the method of Example 9 to approximate the zero correct to two decimal places.f(x) = 3x3 - 2x2 - 20
In problem, analyze each polynomial function f by following Steps 1 through 8.f(x) = x4 - 2.5x2 + 0.5625
In problem, graph each polynomial function.f(x) = x3 + 2x3 - 5x - 6
The illustration shows the graph of a polynomial function.(a) Is the degree of the polynomial even or odd?(b) Is the leading coefficient positive or negative?(c) Is the function even, odd, or
In problem, analyze each polynomial function f by following Steps 1 through 8.f(x) = x4 - 18.5x2 + 50.2619
In problem, graph each polynomial function.f(x) = x3 + 8x2 + 11x - 20
In problem, analyze each polynomial function f by following Steps 1 through 8.f(x) = 2x4 – πx3 + √5x – 4
In problem, graph each polynomial function.f(x) = 2x3 + x2 + 2x + 1
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = 4x - x3
In problem, graph each polynomial function.f(x) = x4 + x2 - 2
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = x - x3
In problem, graph each polynomial function.f(x) = x4 - 3x4 - 4
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = x3 + x2 - 12x
In problem, graph each polynomial function.f(x) = 4x4 + 7x2 - 2
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = x3 + 2x2 - 8x
In problem, graph each polynomial function.f(x) = 4x4 + 15x2 - 4
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = 2x4 + 12x3 - 8x2 - 48x
In problem, graph each polynomial function.f(x) = x4 + x3 - 3x2 - x + 2
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = 4x3 + 10x2 - 4x - 10
In problem, graph each polynomial function.f(x) = x4 - x4 - 6x4 + 4x + 8
In problem, analyze each polynomial function by following Steps 1 through 6.f(x) = -x5 + 5x4 + 4x3 - 20x2

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