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Math 105 Exam 3
Given: Standard form for a quadratic:
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
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.).
For what value of w is the area largest? w =_________. What is the maximum area? A=__________
|zeros|| Multiplicity for
for each zero
(odd or even)
(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 = _________
This function is: odd even neither (circle one)