Section 8.8
Linear Programming
OBJECTIVE 1
OBJECTIVE 2
Consider the linear programming problem
Maximize: I = 0.05 x + 0.08 y
subject to the conditions that
x0
y0
x + y 30
x 20
y 5
Minimize the expression z = 3 x + 4 y
subject to the constraints
y7
x 10
x+
Section 6.2
One-to-One Functions;
Inverse Functions
OBJECTIVE 1
Car
Saturn
John
Pontiac
Joe
(a)
Student
Dan
Honda
Andy
(b) cfw_(1,5), (2,8), (3,11), (4,14)
For each function, use the graph to determine whether the function
is one-to-one.
(a)
(b)
A functio
Section 6.1
Composite Functions
OBJECTIVE 1
Suppose that an oil tanker is leaking oil and we want to be
able to determine the area of the circular oil patch around the
ship. It is determined that the oil is leaking from the tanker
in such a way that the r
Section 5.6
Complex Zeros;
Fundamental Theorem of
Algebra
OBJECTIVE 1
A polynomial of degree 5 whose coefficients are real numbers
has the zeros -2, -3i, and 2+4i. Find the remaining two zeros.
OBJECTIVE 2
Find a polynomial f of degree 4 whose coefficient
Section 5.5
The Real Zeros of a
Polynomial Function
OBJECTIVE 1
Find the remainder if f ( x ) = x + 3 x + 2 x 1 is
divided by
(a) x + 2
(b) x 1
3
2
Use the Factor Theorem to determine whether the function
f ( x ) = -2 x 3 - x 2 + 4 x + 3 has the factor
(a
Section 5.4
Polynomial and Rational
Inequalities
OBJECTIVE 1
Solve ( x + 3)
2
( x 1) ( x 4 ) 0
Solve the inequality ( x + 3 )
and graph the solution set.
2
( x 1) ( x 4 ) 0 algebraically,
OBJECTIVE 2
x4
Solve
2 by graphing.
x+2
Solve the inequality
x4
2
Section 5.3
The Graph of a Rational
Function
OBJECTIVE 1
x2 4
Analyze the graph of the rational function: R ( x ) = 2
x + 3x 4
x 2 + 3x + 2
R ( x) =
x
x 2 x + 12
R ( x) =
2
x 1
x2 9
R ( x) = 2
x + 9 x + 18
OBJECTIVE 2
Section 5.2
Properties of Rational
Functions
OBJECTIVE 1
Find the domain of the following rational functions:
x2 4
(a) R ( x ) =
x+4
x 5
(c) R ( x ) = 2
x +2
x+6
(b) R ( x ) = 2
x + 8 x + 12
x2 9
(d) R ( x ) =
3
x2 4
(e) R ( x ) =
x+2
Graph the rational f
Section 5.1
Polynomial Functions
and Models
OBJECTIVE 1
(a) f ( x ) = 3 x 5 4 x 4 + 2 x 3 + 5
1
3
(b) g ( x ) = 3 x 2 + 5 x 10
(c) h ( x ) = 3 x 5
(d) F ( x ) = 2 x 3 + 3 x 8
(e) G ( x ) = 5
(f) H ( s ) = 3s ( 2s 2 1)
Summary of the Properties of the Grap
Section 4.5
Inequalities Involving
Quadratic Functions
OBJECTIVE 1
Solve the inequality 2 x 2 5 x + 2 > 0
and graph the solution set.
Solve the inequality 2 x 2 4 x + 5 and graph the solution set.
Section 4.4
Building Quadratic Models
from Verbal Descriptions
and Data
OBJECTIVE 1
x = 26, 000 160 p
800
(a) Find the maximum height
of the projectile.
(b) How far from the base of
the cliff will the projectile
strike the water?
OBJECTIVE 2
Section 4.3
Quadratic Functions and
Their Properties
OBJECTIVE 1
f ( x ) = 2 x 2 + 6 x + 2
OBJECTIVE 2
Without graphing, locate the vertex and axis of symmetry of the
parabola defined by f ( x ) = 3 x 2 + 12 x 5. Does it open up or down?
OBJECTIVE 3
Graph
Section 4.2
Building Linear Models
from Data
OBJECTIVE 1
(a) Draw a scatter
diagram of the data,
treating on-base
percentage as the
independent variable.
(b) Use a graphing utility
to draw a scatter
diagram.
(c) Describe what
happens to runs scored
as the
Section 4.1
Linear Functions,
Their Properties,
and Linear Models
OBJECTIVE 1
3
Graph the linear function f ( x ) = x + 5
2
What is the domain and the range of f?
OBJECTIVE 2
OBJECTIVE 3
Determine whether the following linear functions are increasing,
dec
Section 6.3
Exponential Functions
OBJECTIVE 1
OBJECTIVE 2
Graph f ( x ) = 2 x +1 4 and determine the domain, range,
3
and horizontal asymptote of f .
OBJECTIVE 3
Graph f ( x ) = e x 2 and determine the domain, range,
and horizontal asymptote of f .
OBJECT
Section 6.4
Logarithmic Functions
OBJECTIVE 1
(a) 58 = t
(b) x 2 = 12
(c) e x = 10
(a) y = log 2 21
(b) log z 12 = 6
(c) log 2 10 = a
OBJECTIVE 2
( a ) log3 81
1
( b ) log 2
8
OBJECTIVE 3
( a ) f ( x ) = log 3 ( x 2 )
x+3
( b ) F ( x ) = log 2
x 1
( c
Student: ahmed khalaf Instructor: Stephanie Smith Assignment: HW Chapter R.3
Date: 5/21/16 Course: mat151_10525
Time: 1:39 PM Book: Bittinger: College Algebra: Graphs
& Models, 5e
1, Determine the degree of each term of the polynomial, the leading term,
Student: ahmed khalaf Instructor: Stephanie Smith Assignment: HW Chapter R.5
Date: 5/21/16 Course: mat151_10525
Time: 1:45 PM Book: Bittinger: College Algebra: Graphs
& Models, 5e
1, Solve the equation. x = 28
(Type an integer or a decimal.)
x - 3 = 2
Section 7.4
The Hyperbola
OBJECTIVE 1
Find an equation of the hyperbola with center at the origin, one
focus at ( 5, 0), and one vertex at (2, 0). Graph the equation.
2
2
x
y
Use a graphing utility to graph the ellipse
=1
36 25
x2 y 2
Analyze the equation
Section 7.3
The Ellipse
OBJECTIVE 1
Find an equation of the ellipse with center at the origin, one
focus at (0, 3) and a vertex at (5, 0). Graph the equation.
2
2
x
y
Use a graphing utility to graph the ellipse
+
=1
36 25
x2 y 2
Analyze the equation:
+
=1
Section 7.2
The Parabola
OBJECTIVE 1
Find an equation of the parabola with vertex at (0, 0) and focus at
(4, 0). Graph the equation.
Graph the parabola y = 16 x.
2
Analyze the equation y = 10 x.
2
Analyze the equation x = 8 y.
2
Find the equation of the p
Section 6.9
Building Exponential,
Logarithmic, and Logistic
Models from Data
OBJECTIVE 1
Table on next slide
OBJECTIVE 2
Table on next slide
OBJECTIVE 3
Table on next slide
Section 6.8
Exponential Growth and
Decay Models;
Newtons Law;
Logistic Growth and Decay
Models
OBJECTIVE 1
A colony of bacteria grows according to the law of
uninhibited growth according to the function N ( t ) = 90e0.05t ,
where N is measured in grams an
Section 6.7
Financial Models
OBJECTIVE 1
A credit union pays interest of 4% per annum compounded quarterly
on a certain savings plan. If $2000 is deposited in such a plan and the
interest is left to accumulate, how much is in the account after 1 year?
Fin