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( )