# Algebra homework help

Algebra homework help. Math 141 Exam 2: 3.5 – 5.7 Name:________________________
SCIENTIFIC CALCULATORS ONLY!!! YOU MUST SHOW WORK FOR CREDIT!!! BOX ANSWERS!
1. [4 pts] Graph �(�) = − !
” √� + 2 + 3. Label 3+ points.
a) [1 ea] Compared to � = √� , we can conclude it:
i) has endpoint: ( , )
ii) has shifted ______ units UP DOWN
iii) has shifted ______ units Left Right Neither
iv) is Stretched/Thinner Normal Compressed/Wider
v) is reflected (“flipped upside-down”): YES NO
b) [1 ea] Find: intercept(s) : intercept:
c) [1 ea] Find: Interval(s) where the function is
i) increasing: ii) decreasing:
d) [2 pts] Find any local extrema (indicate max/min):
e) [1;1] Domain:
Range:
f) [1 pt] Even, Odd, or Neither?
g) [2 pts] Find any absolute extrema (indicate max/min):
x – y –
2. You have 500 ft roll of fencing and a large field. You want to construct a rectangular playground. Include units.
a) [8] Find the dimensions. b) [5] What is the maximum area of the playground?
3. [8 points] A rectangle is inscribed in a circle of radius 1. Let P=(x,y) be the point in quadrant I that is a vertex of the
rectangle and is on the circle.
a) Express the area of the rectangle as a function of x.
b) Express the perimeter p of the rectangle as a function
of x
4. Let �(�) = 2�# + 2�\$ − 11�” + � − 6
a) [2] What is the maximum number of real zeros?
b) [2] List all possible rational zeros.
c) [10] if one zero is −3, find all remaining zeros.
EXTRA CREDIT [6 points]: Find for �(�) = !
“!. Simplify! fx h fx ( ) ( )
h
+ –
5. [8;10] Solve – use “zones” or sign-chart. Graph solution on a number line and express in Interval Notation.
a) �\$ + 2�” − 3� > 0 b) “#\$
%”&!
≤ 3
6.�(�) = !
%
�\$ − #
%
�” − 5� + 20 x c) [5] Sketch
a) [5] Find the zeros of :
b) [1] Find the intercept: ( , )
d) [2] “End Behavior”: i) As , ________.
ii) As , ________.
P x( ) P x( )
P x( )
y –
x ® -¥ P x( ) ®
x ® ¥ P x( ) ®
7. [15 pts] Given �(�) = “!#”&!%
“!&\$ , find
a) Zero(s):
b) Vertical Asymptote(s):
c) Horizontal OR Oblique Asymptote
(identify which one it is as well):
d) Sketch
8. [6 ea] Find the domain of the following in interval notation:
a) �(�) = √�\$ − 3�”
b) �(�) = 4&’!
&(#
R x( )
x R x( )

Algebra homework help

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