Exam 4: Polynomial and Rational Functions

For the rational function f (x) = , find the equation of the slant asymptote.

Find all the real zeros (and state their multiplicity) of the polynomial function.

For the polynomial function, (a) list each real zero and its multiplicity; (b) determine whether the graph touches or crosses at each x-intercept; (c) find the y-intercept; (d) determine the end behavior; and (e) sketch the graph.

Find the vertex of the parabola associated with the quadratic function. Y = + 10

Use Descartes' rule of signs to determine the possible number of positive real zeros, negative real zeros, and imaginary zeros.P(x) = - 3 + 3x + 6

Find the standard form of the equation of a parabola whose vertex is (8, 4.1) and passes through the point (-2.5, 158.45).

For the given graph: (a) list each real zero and its smallest possible multiplicity; (b) determine whether the degree of the polynomial is even or odd; (c) determine whether the leading coefficient of the polynomial is positive or negative; (d) find the y-intercept; (e) write an equation for the polynomial function (assume the least degree possible).

Find all zeros (real and complex). Factor the polynomial as a product of linear factors.

Find the standard form of the equation of a parabola whose vertex is (2, 9) and passes through the point (7, -116).

Find a polynomial of minimum degree that has these zeros.

Use the graphing strategy to graph the rational function.

Find all the real zeros (and state their multiplicity) of the polynomial function.

Find the vertex of the parabola associated with the quadratic function. Y = -5 + 8

Determine whether the number -7 is a zero of f (x) = + 3 - 36x + 32. If it is, find the other real zeros.

The concentration of a drug in the bloodstream, measured in parts per million, can be modeled with a quadratic function. In 67 minutes the concentration is 49.266 parts per million. The maximum concentration of the drug in the bloodstream occurs in 300 minutes and is 375 parts per million. -In how many minutes will the drug be eliminated from the bloodstream?

Rewrite the quadratic function in standard form by completing the square. y = 4 - 48x + 130

Professor Ito is teaching a large lecture course and is trying to learn students' names. The number of names he can remember, N(t), increases with each week in the semester, t, and is given by the rational function:N(t) = How many students' names does Professor Ito know by the fourth week of the semester? How many students' names should he know by the end of the semester (16 weeks)? Round your answer to the nearest whole number.

Graph the quadratic function.

A person standing near the edge of a cliff 150 feet above a lake throws a rock upward with an initial speed of 40 feet per second. The height of the rock above the lake at the bottom of the cliff is a function of time and is described -At what time will the rock hit the water? Round to two decimal places.

Determine whether -5 is a zero of the polynomial. If it is, then find the other real zeros.P(x) = + 4 - 4x + 5