THE DIFFERENCE QUOTIENT
I. The ability to set up and simplify difference quotients is essential for calculus students. It is from the difference quotient that the elementary formulas for derivatives are developed. II. Setting up a difference quotient for
Does the given relation define y as a function of x? Why, or why not?
a.
b.
y
0
1
2
1
4
1
6
1
8
c.
x
1
y = x+4
Find the domain and range.
a.
b.
x + 1 3 x 2
f (x) =
x2
x >2
x y
0 1
1 2
2 3
0 4
1 5
c.
y=
d.
f
g
x 3
(x) where f (x) = x 2 and g(x) = x
Grap
1.
5/ 2 2/ 5 10
w x
.
Simplify
w5x
2.
Factor completely over the integers: 42x 5 + 16x 4 10x 3 .
3.
Write as a single fraction with a simplified numerator:
4.
Multiply x 2 1 x 2/ 3 out fully, writing your answer with only natural number
x
3x 2 x 2 1
Does the given relation define y as a function of x? Why, or why not?
a. No. The graph does not pass the vertical line test.
b. Yes. For each x value in the domain, there is only one y value.
c. Yes. For each x value in the domain, the formula yields a si
MATH 1150
Test #1 Review Sheet
Answer Key
1.
a. F
i. F
2.
a.
cfw_11
c.
cfw_
3.
b. F
j. F
c. F
k. F
b.
64 , 9 ,
a. 12
b. 13
( 0 , 0 ); 4
c.
(x 3) + (y + 5)
b.
2
2
2
27b 30
a
2x
9
2
b. 15
d.
2
2
2
2
b.
(x 2) + (y 3)
= 61
d.
(x + 3) + (y 2)
c.
y
x
2
d.
(
MATH 1150
Test #1 Review Sheet
Fall 2011
This review sheet is intended to aid you in your review and study for the first test. It is not
intended to be a complete list of topics covered, nor to give a model of every problem type
which might appear on the
MATH 1150
1.
a.
c.
d.
Test #3 Review Sheet
Answer Key
Fall 2011
Note: you may have chosen a different domain for the single period to sketch than what is shown below.
b.
e.
1.
f.
g.
h.
i.
k.
j.
l.
2.
a.
4
b.
3.
a.
90
b.
20
4.
a.
128 is coterminal to 0, an
MATH 1150
Test #3 Review Sheet
Fall 2011
This review sheet is intended to aid you in your review and study for the third test. It is not intended to be a
complete list of topics covered, nor to give a model of every problem type which might appear on the
MATH 1150
Test #2 Review Sheet
Answer Key
1.
a.
A = 9x 2 4
b.
A = x 2 16
2.
a.
x 1 and x 10
b.
x 5
e.
(3, 3)
f.
Fall 2011
2,5) (5,)
3.
a.
3,)
c.
b.
c.
d.
(,3 3,)
d.
e.
f.
g.
h.
i.
j.
k.
l.
3.
m.
n.
o.
p.
4.
a.
e.
1:1 function
1:1 function
b. function, n
MATH 1150
Test #2 Review Sheet
Fall 2011
This review sheet is intended to aid you in your review and study for the first test. It is not intended to be a
complete list of topics covered, nor to give a model of every problem type which might appear on the
1-london bridge tower:
-The London Bridge Tower, also known as the Shard, is a 72-storey,
mixed-use tower located beside London Bridge Station on the south bank of the
river Thames. This project was a response to the urban vision of London Mayor
Ken Livin