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Math 3304 Basics Homework - HOLLYER
Name:
You are encouraged to work together on problems sharing ideas and – hopefully, arguing
your way through. Please give credit where it is due, though, if someone’s email or post
helped you out!
Keep your answers in order and work on the front side only. If you need to insert
additional pages, then put them in the proper order. Please work neatly; if it’s illegible,
then the grader has instructions to award a zero on that work*.
This is a 145 point assignment. 10 of these points are neatness points – to be awarded
at the grader’s discretion (see above*). Be neat and legible, please. Don’t skimp on
paper; it needs to be easy to grade.
This assignment is due by noon on the Monday listed in the course calendar on my
website. No late homework will be accepted for any reason.
Please submit the homework, in a single pdf file, to the assignments tab in your
courseware accout.
GRADE:
Work (135)
______
Neatness (10)
______
Total
______
1
12 points (4 for A; 8 for B)
1.
A.
Let A be the set of all real numbers.
Let B also be the set of all real numbers.
What is the resulting set for A B?
Sketch the picture framework.
B.
Let A = {0, 1, 2, 3, 4}, B = {xx is an even natural number},
C = {x1 < x < 6, x is a real number}, and
D = {xx > 0, x is a multiple of 3 and is a natural number}.
AB=
AC=
CD=
(B  C)  A =
2
Problem 2
2A.
32 points total, 8 each part (3 list, 2 graph, 2 bounds)
1
Given { n is a natural number}.
n
Give a list of set elements that is at least 6 elements long.
Use appropriate notation.
Make a 2 D graph of this set showing at least 6 point pairs.
Discuss the bounds? Where is the set bounded or unbounded. Include a sentence
indicating HOW you know this. If there is a glb or a lub, be sure to label it
clearly.
3
2B
Given {(10)n n is a natural number}
Give a list of set elements that is at least 6 elements long.
Use appropriate notation.
Make a 2 D graph of this set showing at least 6 point pairs.
Discuss the bounds? Where is the set bounded or unbounded. Include a sentence
indicating HOW you know this. If there is a glb or a lub, be sure to label it
clearly.
4
2C
Given {2 n n is a natural number}
Give a list of set elements that is at least 6 elements long.
Use appropriate notation.
Make a 2 D graph of this set showing at least 6 point pairs.
Discuss the bounds? Where is the set bounded or unbounded. Include a sentence
indicating HOW you know this. If there is a glb or a lub, be sure to label it
clearly.
5
2D
Given {(n  1)n1 n is a natural number}
Give a list of set elements that is at least 6 elements long.
Use appropriate notation.
Make a 2 D graph of this set showing at least 6 point pairs.
Discuss the bounds? Where is the set bounded or unbounded. Include a sentence
indicating HOW you know this. If there is a glb or a lub, be sure to label it
clearly.
6
3.
Find the domain, x-intercept(s) and y-intercepts for the following functions.
48 points
(6 points each part – 2 per answer)
a.
f ( x) 
1
1
x
3
2
Domain
Work:
x-intercept
Work:
y-intercept
Work:
7
b.
f (x)  x 2  x  6
Domain
Work:
x-intercept
Work:
y-intercept
Work:
8
c.
f (x) 
1
2 x  18
Domain
Work:
x-intercept
Work:
y-intercept
Work:
9
d.
f (x)  5x 3  125
Domain
Work:
x-intercept
Work:
y-intercept
Work:
10
e.
f (x) 
2x  36
x9
Domain
Work:
x-intercept
Work:
y-intercept
Work:
11
f.
f ( x )  9  3x
Domain
Work:
x-intercept
Work:
y-intercept
Work:
12
g.
f (x) 
1
2x  x  3
2
Domain
Work:
x-intercept
Work:
y-intercept
Work:
13
h.
f (x) 
1
6x  11x  3
2
Domain
Work:
x-intercept
Work:
y-intercept
Work:
14
4.
** points
Evaluate the following functions for the given x value.
List the domain and the range on the sketch in interval notation.
Label any asymptotes or state that there are none.
Sketch the graph:
Feel free to use a graphing calculator or program.
(MathGV is a nice program and it’s free.)
4A
8 points
f (x)  3  x
f(1) =
f(0) =
f(1/2) =
Domain:
Range:
Sketch (2 points):
Asymptotes?
15
4B
8 points
f (x)  x  x 2
f(1) =
f(0) =
f(1/2) =
Domain:
Range:
Sketch (2 points):
Asymptotes?
16
4C
9 points
f ( x )  ( x  2) 1
f(1) =
f(0) =
f(1/2) =
f( ¾) =
Domain:
Range:
Sketch (2 points):
Asymptotes?
17
4D
9 points
f ( x )  8x
f(1) =
f(0) =
f(1/3) =
f(1/2)
Domain:
Range:
Sketch (2 points):
Asymptotes?
18
4E.
9 points
f (x)  x 3  2x 2  5x  6 *
*hint: (x +1) is a factor
Factored form:
f(1) =
f(0) =
f(1/2) =
Domain:
Range:
Sketch (2 points):
Asy
19