New York University
Algebra and Calculus, Fall 2011
Review Problems for Midterm 2
Exam 2 covers 3.1, 3.2, 3.3, 3.4, 3.7, 4.1, 4.2, 4.3, 4.4, 4.5
1. Find a quadratic function that has zeros at x = 2 and x = 1 and passes through the point (-4,2).
f (x) = a(
Precalculus-Homework Assignment 7
Due Thursday 10th, beginning of class
Covers 4.1-4.4
Gemma Huguet
New York University
Read Sections 4.1-4.4
Do the following problems from the Textbook:
Please make sure you write out the solutions neatly. Please show all
Precalculus-Homework Problems - Stepp
HW #8
(1) Section 4.3 Problem 85
(2) Section 4.3 Problem 90
(3) Find a formula for an exponential function y = kax with y-intercept at 10 and whose graph passes
through the point (3,20).
(4) Let f (x) = 5 + 3 2x . As
New York University
Algebra and Calculus, Fall 2012
Review Problems for Final Exam
Problems from the book
Section
Section
Section
Section
Section
5.1:
5.2:
5.3:
5.4:
5.5:
23-25, 35, 36, 40-43
5-8, 25, 55-60
35-40
58
1-10, 23-30, 39-44
Section 6.1: 3-6, 15
3
1
2
x=2
3
x
x = 1 x = Precalculus-Homework Problems - Stepp
2
HW #8
y
x = 1
(1) Find possible formulas for the two following functions:
y
38.
x=1
x = 2
2
x
2
y
36.
x
y
x=3
!
3
x
(0, 3)
18 11x + x2
y a
y 1
graph of f (x)=
is a line withx= 1
x 2
2
3
3
e i
Please grade as following: For 35, 77, 40 and 34 please grade out of 3 points each:
5. 6 points
a) 2.9;
b) (2.2, 2.9) and (6.1, 4.9) answers may vary
c) 0, 4,8 zeros or roots or x-intercepts
d) y = 0
e) f(4) = 0 and f(6.1) = 4.9
f) x = 2.2 and x = 6.1
6.
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cos t = sin t +
2
= sin
t = cos(t)
2
Pythagorean Identity
Precalculus-Homework 9
cos2 t New York 1
+ sin2 t = University
Hand in the following problems. Do not forget to:
Tangent and Cotangent
I Write your section number on your assignment;
sin t
1
tan
In Problems 2332, give a possible formula for the polyno11.3 THE SHORT-RUN BEH
New York University
11.3 POLYNOMIALS
11.3 THE SHORT-RUN BEHAVIOR OFTHE SHORT-RUN BEHAVIOR
453
mial.
Algebra and Calculus, Fall 2012
In Problems 2332, give aReview Problems for
New York University
Algebra and Calculus, Fall 2013
Some Important Topics for the Final
1. General:
(a) Know the graph of every base function we worked on
(b) Know how to nd the x-intercept(zero) and the y-intercept of a function
(c) Know how to determine
Precalculus-Homework Problems - Stepp
HW #6
(1) Section 3.2 Problems 26,34,80
(2) Section 3.3 Problem 24,46
(3) Find a fourth-degree polynomial P (x) that has zeros at x = 0, x = 1, x = 1, and x = 2 and
whose x2 -term has coecient 5.
Solution: P (x) = ax(
All about Functions
OBJECTIVES:
1. State clearly and precisely the denition of a function.
2. Given any function, be able to express the functions in all of the four representations.
3. Find the domain and range of a given function algebraically.
4. Deter
Worksheet Piecewise Functions
Algebra 2
Name:
Part I. Carefully graph each of the following. Identify whether or not he graph is a function. Then,
evaluate the graph at any specified domain value. You may use your calculators to help you graph, but you
mu
The Algebra of Functions
OBJECTIVES:
1. Compute the sum and dierence of functions and determine the domain of the result.
2. Compute the product and quotient of functions and determine the domain of the result.
3. Compute the composition of two functions
New York University
Algebra and Calculus, Fall 2011
Review Problems for Midterm 1
1. Find all x that satisfy given inequalities.
(a) 2x 4 0
(b) x2 4x + 3 0
(c) x2 3x 4 > 0
(d)
(e)
x+2
x(x2)
2
x
x 2 4
>0
0
(a)
2x
x
4
2
Dont forget to ip the sign when divid
New York University
Algebra and Calculus, Fall 2011
Material for the Final and Practice Final
1. General:
(a) Know the graph of every base function we worked on
(b) Know how to nd the x-intercept(zero) and the y -intercept of a function
(c) Know how to de
HW-2-Solutions
Page 1
HW-2-Solutions
Page 2
Job: 1-3pt18-main Sheet: 1 Page: 1 (September 21, 2011 11 : 59) [1-3pt18-main]
1
1-3pt18
3)
1. Sri Lanka is an island that experienced approximately linear population growth from 1950 to 2000. On the
other hand,
Page 1
Page 2
9) The graph of f (x) contains the point (3,-4). What point must be on the graph of
1. f (x) + 4(3,0)
2. f (x + 5)(-2,-4)
3. f (x 3) 2(6,-6)
4. f (2x + 4) 3(-0.5,1)
10)
Using the table below, make tables for the following transformations of
Precalculus-Homework Assignment 4
Due Thursday 20nd, beginning of class
Covers 3.1
Gemma Huguet
New York University
Read Section 3.1
Do the following problems from the Textbook:
Please make sure you write out the solutions neatly. Please show all your wor
Precalculus-Homework Assignment 5
Due Thursday 27th, beginning of class
Covers 3.2-3.3-3.4
Gemma Huguet
New York University
Read Sections 3.2-3.3-3.4
Do the following problems from the Textbook:
Please make sure you write out the solutions neatly. Please
Precalculus-Homework Assignment 6
Due Thursday 3rd, beginning of class
Covers 3.7
Gemma Huguet
New York University
Read Sections 3.7
Do the following problems from the Textbook:
Please make sure you write out the solutions neatly. Please show all your wor
Pythagorean Identity
cos2 t + sin2 t = 1
Tangent and Cotangent
Precalculus-Homework Assignment 8
Due Thursday December 1, beginning of class
sin t
1
tan t = Covers 5.1-5.2
=
cosGemma Huguet
t
cot t
1
cos t
York University
cot t = New =
sin t
tan t
Read
rves in Figure 7.87 model three differB
6-2pt32
35.
: (i) moderately heavy trafc with some 6-1pt32tab h 4.0 5.2 6.2 6.5 6.2
stop-and-go rush-hour trafc; and Precalculus-Homework Assignment 9 10 11 12
(iii)
t C8
9
6-miscpt1fig1
Due Thursday December 8, beg