I need help with final exam

Math 141 Exam Final Exam Name:_____________________________

SCIENTIFIC CALCULATORS ONLY! YOU MUST SHOW WORK FOR CREDIT!!! BOX ANSWERS!

1. [6 ea] Factor completely; simplify.

a) 12π₯

!

” β 5π₯

#

” β 2 b)3(4π₯ + 5)! β 2(4π₯ + 5) β 1

2. [4 each (a-e)] Approximate if necessary. For the given function , find/determine:

a) Domain: Range:

b) On what interval(s) is π:

i) Increasing:

ii) Decreasing:

c) ______ when ______.

d) Find any relative extrema (tell me if you have a max or min, what it is, and where it is):

e) Find any absolute extrema (tell me if you have a max or min, what it is, and where it is):

f) [2] Is π even, odd , or neither? g) [4] What is the end behavior?

h)[4] What are the x and y- intercepts?

( )f x

( )2f – = ( ) 4f x = x =

3. [8 pts] a) Graph the function 4. [1 ea] Given π(π₯) = β”

!

|π₯ + 3| β 1

π(π₯) = /

2 β π₯, β3 β€ π₯ < 1
π₯! β 2π₯ + 2, π₯ > 1

. Label 3+ points. Explain how the graph of π(π₯) is obtained from the graph

π(π₯) = |π₯|. (Hint: four actions=transformations)

a)

b)

c)

d)

5. [8;6] Given that

π(π₯) = #

$

, β(π₯) = log(π₯ + 1) , π(π₯) = !

$%”

, π(π₯) = βπ₯ β 10

find the following and their DOMAINS. Use Interval Notation! and simplify the function when possible.

a) b)

6. [14 pts] Given π (π₯) = &$

$#%$%”!

find:

a) Zero(s):

b) Vertical Asymptote(s):

c) Horizontal OR Slant Asymptote: d) Sketch . You do not need

specific values except for zero(s) and

asymptote. The shape needs be accurate!!!

j! f( ) x( ) ( )

( )

h x

g x

( )R x

y-

( )R xx

7. [9] Let π(π₯) = 2π₯’ β 9π₯! + 7.

a) List all possible rational zeros.

b) Find the remaining zeros of if one zero is β1.

8) [8] Solve the inequality π₯& + 2π₯! β 3π₯ > 0. Graph the solution on a number line and state the solutions in interval

notation.

9. [8 pts] A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions inches

by inches by cutting out equal squares of side at each corner and then folding up the sides as in the figure.

Express the volume of the box as a function of and simplify completely.

( )p x

8

20 x

V x

x

x

10. [10 pts] Find for π(π₯) = !

“#$

. Simplify!

11. [9 pts] Solve – use βzonesβ or sign-chart. Graph solution and express in Interval Notation.

%

“&’

β₯ (

“&)

12. [8 pts] A landscape engineer has 200 feet of border to enclose a rectangular pond. What dimensions will result in the

largest pond?

( ) ( )f x h f x

h

+ –

13. a) [4 pts] Express in terms of individual logarithms. b) [4 pts] Express as a single logarithm.

Simplify, if possible. Simplify, if possible.

ln)”

!β”&!

(“#!)”

* 4ln(5π₯ β 4) β 3ln(x + 2) β $

!

ln (x)

14. [8 pts]Find the first term and the common difference of the arithmetic sequence described. Find a formula for the

nth term.

15. [8 pts] Given: 4 + 3 + (

‘

+ !)

“*

+ β―

a) Determine whether the following series is arithmetic b) Find the sum of the series.

or geometric. If arithmetic, find its common difference,

, and if geometric, find its common ratio, .

16. [4 pts] Express the sum using summation notation.

17. [8 pts] Find the exact sum of .

d r

1

2

β

2

3

+

3

4

β!+

11

12

( )

13

3

1k

k kp

=

+Γ₯