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Math 105 Exam 3

Given: Standard form for a quadratic:   QF: , the
Odd (origin symmetry): f(– x) = – f(x), Even (y-axis 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 y-intercept? ______________

 

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 x-axis or b.) touch the x-axis 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 =
x-intercept(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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