# Algebra and Trigonometry

Mathematics

## Quiz 4 :Polynomial and Rational Functions

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For the following function, find a number such that the graph of contains the point
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B

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Find all solutions of the equation.
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D

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Sketch the graph of .
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D

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Find all values of such that
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A meteorologist determines that the temperature T for a certain 24-hour period in winter was given by the following formula. is time in hours and corresponds to 6 A.M.
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Show that the number is a zero of of the given multiplicity, and express as a product of linear factors.
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Use the remainder theorem to find ,
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Use the factor theorem to decide whether is a factor of the polynomial. ;
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Find the polynomial function of degree whose graph is shown in the figure.
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Find the quotient and remainder if is divided by . ,
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A herd of 575 deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. Suppose that the number of deer after years is given by the following formula. where How many years does it take for the population to become extinct?
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An aspirin tablet is in the shape of a right circular cylinder. The manufacturer also wishes to market the aspirin in capsule form. The capsule is to be centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If denotes the radius of a hemisphere, find a formula for the volume of the capsule.
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Find a polynomial with leading coefficient of , degree , and zeros: - .
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An arch has the shape of the parabola A rectangle is fit under the arch by selecting a point on the parabola (see the figure). If the rectangle has base and height . Find the base of a second rectangle that has the same area.
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Use synthetic division to decide whether is a zero of ;
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Does there exist a polynomial of degree 3 with real coefficients that has zeros 9 , - 9, and i ?
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Sketch the graph of for the indicated value of .
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Find all solutions of the equation.
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