Without graphing, describe the end behavior the polynomial.
a) When calculations are involved, show how you came up with your answers.
b) Show why you choose certain answer for true-or-false and multiple-choice questions.
c) Answers that come straight from programs or software packages will not be accepted.
d) In order to receive full credit, make sure that each answer is as complete as possible.
Problem 1. Without graphing, describe the end behavior the polynomial.
f(x)=-3x^2+4x-1
Problem 2. Find a polynomial function P(x)with least possible degree and integer coefficients that satisfies the following conditions:
Zeros 5 and -2
Problem 3. Graph the following function by transforming the appropriate function of the form y=x^n. Then, give the domain and range.
f(x)=-(x+3)^2
Problem 4. Write the following function in vertex form, then give the vertex, domain, range, and open intervals where the graph is increasing and decreasing. Finally, graph the function.
f(x)=x^2+6x+4
Problem 5. Write the following function in vertex form, then give the vertex, domain, range, and open intervals where the graph is increasing and decreasing. Finally, graph the function.
f(x)=-x^2+2x-1
Problem 6. Mark has 120 feet of fence to make a rectangular pen for his chickens. If the coop will account for one side of the pen, what dimensions would make for the maximum area?
Problem 7. Factor the following polynomial to find all of its x- intercepts.
P(x)=x^2+7x
Problem 8.Find a polynomial function P(x)with least possible degree and integer coefficients that satisfies the following conditions.
Zeros 5 and -2
Problem 9. Give the equations of any asymptotes for the following rational function, then graph.
f(x)=3/(5x+3)
Problem 10.Solve the following inequality.
(x+3)/(x-2)>0
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