Exam 3: Polynomial and Rational Functions

Use the following to answer questions : y varies directly with x; y = 8.4 when x = 24. -Use descriptive variables to write the variation equation for the statement. the time required to complete a job varies inversely as the number of workers

Use the following to answer questions : y varies inversely with x; y = 12,600 when x = 0.2. -Find the constant of variation.

Use the following to answer questions : p(x) = x⁴ - 5x³ + 5x² + 5x - 6 -Use the rational roots theorem to list all possible rational roots.

Use Descartes's rule of signs to determine the possible combinations of real and complex roots for the polynomial. Then graph the function on the standard window of a graphing calculator and adjust it as needed until you're certain all real roots are in clear view. Use this screen and a list of the possible rational zeroes (rational roots theorem) to factor the polynomial and find all zeroes (real and complex). p(x) = 20x³ - 153x² - 62x + 48

Graph the polynomial function. f(x) = x³ + 2x² - 5x - 6

Use the following to answer questions : (Gridlines are spaced one unit apart.) -State the domain of the function.

Use the Guidelines for Graphing Polynomial Functions to graph the polynomial. f(x) = x³ - 3x - 2

For the complex polynomial below, one of its zeroes is x = 3 - i. Use the given zero to help find all zeroes of the polynomial, then write the polynomial in completely factored form. Hint: synthetic division and the quadratic formula can be applied to all polynomials, even those with complex coefficients. C(x) = x³ - 3x² + (3 + 3i)x + (-6 + 2i)

Graph the function using the end behavior, y-intercept, x-intercept(s), vertex, and symmetry. Label the vertex and all intercepts (if they exist). (Round to tenths as necessary). f(x) = -x² + 2x + 5

Use the following to answer questions : (Gridlines are spaced one unit apart.) -Find the minimum possible degree of the function and write it in factored form. Assume all zeroes are real.

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation.

Determine the oblique asymptote if it exists.

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation.

Graph the function. If there is a removable discontinuity, repair the break by redefining the function using an appropriate piecewise-defined function.

Use the intermediate value theorem to verify that the polynomial f(x) = -2x³ - 4x² + 3x - 4 has at least one zero "c_i" in the interval [-3, -1]. Do not find the zeroes.

Use the following to answer questions : An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modeled by the function , where P(x) is the profit in dollars and x is the number of automobiles made and sold. -What is the maximum profit?

Use the following to answer questions : An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modeled by the function , where P(x) is the profit in dollars and x is the number of automobiles made and sold. -Find the x-intercepts and explain what they mean in this context.

Use the following to answer questions : (Gridlines are spaced one unit apart.) -Use the direction/approach notation to describe the end behavior of the graph. (This should produce four statements.)

Use the following to answer questions : (Gridlines are spaced one unit apart.) -State the domain of the function.

Find a quartic polynomial (degree 4) with real coefficients having roots x = -5i and x = i. Assume a lead coefficient of 1.