Linear Functions, Slope and Applications
Objectives
Determine the slope of a line
Work with linear functions
Important Terms and Concepts
model
linear function
identity function
constant function
slope
rise
run
vertical change
horizontal change
rate of ch
Introduction to Graphing
Objectives
Plot coordinate pairs on a Cartesian Coordinate System
Find solutions to a 2-variable linear equation
Determine the intercepts of and graph a 2-variable linear equation
Important Terms and Concepts
Cartesian Coordinate
Symmetry and Transformations
Objectives
Determine the symmetry of a graph with respect to the x- and y-axis
Determine whether a function is even, odd or neither
Transform the graphs of functions using translations, reflections, stretchings and shrinkings
College Algebra Project
Saving for the Future
This project is to be completed individually! If the plaigerism software pings your
assignment as being turned in by another student you will receive a 0 and possibly an XF
for the course. It is very important
Functions and Graphs
Objectives
Determine whether an equation is a function
Calculate function values, or outputs, using function notation
Determine whether a graph is that of a function
Determine the domain and the range of a function
Important Terms and
Quadratic Equations, Functions, and Models
Objectives
Find zeros of quadratic functions
Solve quadratic functions
Solve applied problems using quadratic equations
Important Terms and Concepts
quadratic equations
quadratic functions
Principle of zero produ
Linear Equations, Functions, and Models
Objectives
Solve linear equations
Solve applied problems using linear models
Find zeros of linear functions
Solve a formula for a given variable
Important Terms and Concepts
equation
solve
solution
solution set
The
More on Functions
Objectives
Determine from a graph over what intervals a function is increasing or decreasing
Find the relative maxim and minima
Use functions to model applications - finding the domain, and graphing the function
Graph piecewise functions
Solving Linear Inequalities
Objectives
Solve linear inequalities and compound inequalities
Solve inequalities with absolute values
Solve applied problems using inequalities
Important Terms and Concepts
inequality
solution set
equivalent inequalities
linea
The Algebra of Functions
Objectives
Combine two functions using addition, subtraction, multiplication and division
Determine the domains of the new functions
Find the difference quotient for a function
Find the composition of two functions
Find the domain
Barton Community College
Course Syllabus
Summer 2016
I.
GENERAL COURSE INFORMATION
Course Number: MATH 1834
Course Title: Analytic Geometry and Calculus II
Credit Hours: 5
Prerequisites: MATH 1832 Analytic Geometry and Calculus I with a C or better
Divisi
Prnhlsm #1 : Find the slum end the squnlnn thlt lures thruugh the paints [5.5] end tilt-III
Find out what yen 3.1,;1 and yen:
1232 are
Use the slepe fermuls m= 1'3 J-'1
Plug the paints int-:1 the fems
Pick :1 point rm the equetien cfw_5,6
Use the sl
Question Find the average rate of change of
f(x)=-2x3from -4toO
Formula Average rate of change of x) on interval [gig] is
NJ) -f(a)
ba
Values: A, B and x)
A:-4 , B:O , f(x)=2x3
be) -f(a)
ba
2(o)3(2(4)3)
0_(_4) =-32
Answer:
#2 Suppose the f(x) =3x+5 and g(x)=-2x+15 solve f(x)<g(x)
Steps
Set f(x) to be less than g(x)
3x+5<-2x+15
Subtract 5 on both sides
3x+5<-2x+15
-5
-5
3x<-2x+10
3x<-2x+10
+2x +2x
5x<10
5x
10
<
5
5
X<2
Add 2x to both sides
Divide both sides by 5 to solve for
+
#2 Suppose the x) =31+5 and gcfw_x)=-2x+15 salve f(x<gcfw_x)
Steps
Set fix) to be less than gm
Subtract 5 on both sides
Add 2): to both sides
31+5c-2 x+15
31+5c-2 x+15
-5 -5
3I<-2)t+10
3x<-2x+10
+23: +2):
Silt-<10
Divide both sides by 5 to solve for 1
To break even rix] musr equal c cfw_X
rixi=24x
ctxi= 1000+2D0x
If the variable cost is 5200 24Dx=1000+20x
2401=l+200x
Subtract 2001: from each side to get 1 alone ~2DDx 4001:
40x=100l1
=
Divide each side by 4D to solve for x *9 4"
Answer X=25
240E125:
If the variable cost is $220 2401: 100D+22Dx
240x=10l2l+22x
Subtract 2201: from each side to get it alone -220x 420:
2Dx=1ODEI
2111' 1009
Divide both sides by 20 to solve for x 2" 2"
Answer
240l50=1000+220l50] 12DD=120IJIJ so the break est en point
The data in the accompanying table represent the rate of return of a certain company stock for 11 months, compared with
the rate of return of a certain index of 500 stocks. Both are in percent. Complete parts (a) and (b) below.
=
The above equation is a l
Explanation:
a).
Mode = $55000
mean = $51500
Median = $52500
b).
Mode
$57575
mean
$54075
Median
$55075
All the measues increased by $2575
c).
Mode = $ 57750
Mean = $ 540750
Median = $55125
d).
Mode = $55000
mean = $51500
Median = $52500
A traffic safety company publishes reports about motorcycle fatalities and helmet use. In the first accompanying data table, the
distribution shows the proportion of fatalities by location of injury for motorcycle accidents. The second data table shows th
For the data set shown below. complete parts (a) and (b) below.
x 3 4 5 7 85
y 5 7 8 12 13
(a) Find the estimates of [30 and B1.
[50 z b0 = D (Round to three decimal places as needed.)
[31 3 b1 = D (Round to three decimal places as needed.)
(b) Assuming t
MATHEMATICAL TRIPOS
PART III
Monday, 1 June, 2015 9:00 am to 12:00 pm
PAPER 33
APPLIED STATISTICS
Attempt no more than FOUR questions, with at most THREE from Section A.
There are SIX questions in total.
The questions carry equal weight.
STATIONERY REQUIR
MATHEMATICAL TRIPOS
PART III
Friday, 8 June, 2012 9:00 am to 11:00 am
PAPER 38
TIME SERIES AND MONTE CARLO INFERENCE
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover s
MATHEMATICAL TRIPOS
PART III
Friday, 30 May, 2014 9:00 am to 11:00 am
PAPER 36
TIME SERIES AND MONTE CARLO INFERENCE
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover s
MATHEMATICAL TRIPOS
PART III
Tuesday, 5 June, 2012 1:30 pm to 4:30 pm
PAPER 33
ADVANCED PROBABILITY
Attempt no more than FOUR questions.
There are SIX questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
SPECIAL REQUIR
MATHEMATICAL TRIPOS
PART III
Wednesday, 8 June, 2011 1:30 pm to 3:30 pm
PAPER 29
PERCOLATION AND RELATED TOPICS
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
MATHEMATICAL TRIPOS
PART III
Monday, 4 June, 2012 9:00 am to 11:00 am
PAPER 31
RANDOM MATRICES
Attempt no more than TWO questions.
There are THREE questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
SPECIAL REQUIREMEN
MATHEMATICAL TRIPOS
PART III
Friday, 8 June, 2012 1:30 pm to 4:30 pm
PAPER 29
PRIME NUMBERS
Attempt no more than THREE questions.
There are FIVE questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
SPECIAL REQUIREMENTS
MATHEMATICAL TRIPOS
PART III
Monday, 9 June, 2014 9:00 am to 11:00 am
PAPER 34
NONPARAMETRIC STATISTICAL THEORY
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
MATHEMATICAL TRIPOS
PART III
Wednesday, 4 June, 2014 1:30 pm to 4:30 pm
PAPER 32
BIOSTATISTICS
Attempt no more than FOUR questions, with
at most THREE questions from Analysis of Survival Data.
There are SEVEN questions in total.
The questions carry equal