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Math 105 Exam 3
Given: Standard form for a quadratic:
QF:
, the
Odd (origin symmetry): f(– x) = – f(x), Even
(yaxis symmetry): f(x) = f(– x)
Show All Work for Full Credit!! For all graphs each ticmark is one unit
1. (4 pts ea) Use the method of your choice to solve the following polynomial equations .
2. (4 pts ea) Use interval notation to express the solution set .
3. (5 pts) When three times a number is subtracted from
four, the absolute value of the difference is at
least five . Show your inequality and use interval notation to express the set of
all numbers that satisfy
this condition. No credit for guess and check.
4. (9 pts) Given f(x) = – 3x^2 + 12x – 7 determine without
graphing whether the function has a
minimum or maximum value. circle one : min max. What is that value?
______________
What is the yintercept? ______________
5. (5 pts) You have 520 yards of fencing to enclose a
rectangular plot . Express the area, A, of the
rectangle as a function of w only, and then find the value of w and A (No credit
for guess and check.).
A =____________________________________________.
For what value of w is the area largest? w =_________. What is the maximum area? A=__________
6. (4 pts ea) For the polynomial function list each real
zero and its multiplicity. Then determine at each
zero if the graph will: a.) cross the xaxis or b.) touch the xaxis and turn
around.
zeros  Multiplicity for for each zero (odd or even) 
behavior (a or b) 
7. (4 pts) Divide using long division or synthetic division.
quotient________________ remainder ________
8. (2 pts ea) Use the end behavior to draw a line connecting each polynomial with its possible graph.
9. (5 pts) Given – 1 is a zero of f(x) = x^3 + 13x^2 + 39x
+ 27, then solve : x^3 + 13x^2 + 39x + 27 = 0
Solutions are x =: – 1,
10. (10 pts) For the two given functions identify the following:
Domain of f(x) inany correct notation  
y intercept if any :  y =  y = 
xintercept(s), if any:  x =  x = 
Vertical asymptote(s) if any  x =  x = 
Horizontal asymptote(s) if any  y =  y = 
11. (12 pts) This is a graph of a rational function as it appears on a calculator:
a.) What are the vertical asymptotes?
x = ________ x = _________
b.) As
c.) As
d.) As
e.) As
This function is: odd even neither (circle one)
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