Practice Exam 3

Key

Problem 1  Find the domain of

(x^2-2x-8)/(3x^2+5x-2)

 

Problem 2  The graph is shown below.  Find the domain, range, any intercepts, and any asymptotes.  Then write down a possible function that has this graph.

Graph with vertical asymptote at x=2 and oblique asymptote through (2,0) and (5,2)

 

Problem 3  Find all intercepts, holes, and asymptotes of the given rational function then use the information to graph the equation.

H(x) = (x^2 - 2x - 3)/(x^2-1)

 

Problem 4  Find all intercepts, holes, and asymptotes of the given rational function then use the information to graph the equation.

G(x) = (x^3-9x)/(x^2-2)

 

Problem 5  Use graphical methods to find the solution of

(x^2-x-6)/(x-1) <=0

 

Problem 6  Use Graphical methods to find the solution of

-x^2(x-3)^4(x+2)^3

 

Problem 7  Use algebraic methods to find the solution of

2/(x-4) >= 3/(x-5)

 

Problem 8  Determine the possible number of negative real zeros and the possible number of positive real zeros.  Then list the potential rational zeros.  Do not attempt to find the zeros.

f(x) = 4x^8-9x^7+5x^6-3x^4-2x^3-1

 

Problem 9  Find k such that

f(x) = x^3-kx^2-kx+2

has factor x - 3.

 

Problem 10  Factor

3x^4-11x^3+8x+4

Problem 11  Find a polynomial with a zero at x = 1- i of multiplicity 2 and a zero at x = 4 of multiplicity 3.

 

Problem 12  One of the roots of the polynomial below is 3-i.  Find the rest of the roots.

f(x) = x^4-2x^3-x^2-38x+130

 

Problem 13  Find the zeros (real and complex) of the function.  Then write the function in factored form.

f(x)=x^3+11x^2+43x+65