B
College Algebra
Name
Unit 3b Exam B
Directions: Show all work and reasoning to receive full credit.
Question 0 (1 point): If you had the option to go anywhere in the world, all expenses paid, where would you go?
Why?  __________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
3𝑥 2 − 9𝑥
1) Accurately graph the following function by determining the following: 𝑓 (𝑥 ) =
2𝑥 2 +𝑥−6
a) horizontal or oblique asymptote b) write f in lowest terms
c) vertical asymptote(s) and holes
d) domain and range
1
1
e) x- and y-intercept
d) additional points
2) Accurately graph the following function by determining the following:
a) horizontal or oblique asymptote
b) write f in lowest terms
c) vertical asymptote(s) and holes
d) domain and range
𝑓(𝑥 ) =
𝑥 3 −9𝑥
𝑥 2 +𝑥−6
1
1
e) x- and y-intercept
d) additional points
3) Solve the following inequalities.
5
2
a)
≤
𝑥+2
𝑥−1
b) 𝑥 3 < −3𝑥 2 + 28𝑥
4) The electrical resistance R of a wire varies directly with the length l of the wire and inversely with the square
of the diameter d of the wire. If a wire 246 feet long and 3 millimeters in diameter has a resistance of 2.31
ohms, find the length of a wire of the same material whose resistance is 1.26 ohms and whose diameter is 4
millimeters.
5) Use the function 𝑓(𝑥) = 2𝑥 4 − 9𝑥 3 + 2𝑥 2 − 5𝑥 + 10 to answer the following:
a) Use the rational zeros theorem to list all of the potential rational zeros of the function.
b) Pick two of the zeros from (a) and use the remainder theorem to determine if each is actually a zero of the
polynomial.
6) Analytically determine all of the real zeros of the polynomial function 𝑓(𝑥) = 2𝑥 4 − 2𝑥 3 − 48𝑥 2 + 24𝑥 + 288,
then use the real zeros to factor f as a product of linear factors.
Zeros:_________________________
Factored Polynomial:____________________________________
7) Determine all the zeros in the complex plane for the function 𝑔(𝑥) = 𝑥 4 − 𝑥 3 − 22𝑥 2 + 106𝑥 − 84 and
write the polynomial as a product of linear factors.
Zeros:_________________________
Factored Polynomial:____________________________________
8) Use the zero 2 + 3𝑖 to determine the remaining zeros of the function 𝑓(𝑥) = 2𝑥 4 − 13𝑥 3 + 43𝑥 2 − 53𝑥 − 39
and write the polynomial as a product of linear factors.
Zeros:_________________________
Factored Polynomial:____________________________________
9) Form a polynomial f ( x ) with real coefficients having the given degree and zeros.
Degree: 4; zeros: 2, multiplicity 2; 3 − √2𝑖,
BONUS: Find the equation of the given graph. Leave your answer in factored form.