HW set 6
Answer the question.
How can the graph of f(x) = - x+7
x
be obtained from the graph of f(x)=
First, lets compare f(x) = - x+7 to the basic graph
y= f(x)= x
f(x)= x is a reflection of f(x)= x
Income and Social
Warren Buffet is the man
What is your relationship to money?
Not your shopping orientation, but money
You might think this is tied to income, but
would be wrong
Think of Warren Buffe
Chapter 3: The Normal Distribution
3.15
b
3.36
a:
3.17
b
For example, (, )
3.18 b:
Since the points of inflection are at -1 and 5, and they are one standard deviation away
from 2, the mean
3.19
b
266
Exponential Functions
So far, we have discussed the following types of functions.
Type of Function
Typical Equation
Shape of Graph
Linear
y = mx + b
Line
Quadratic
y = ax2 + bx + c
Parabola
Absolute V
Exponential Functions
So far, we have discussed the following types of functions.
Type of Function
Typical Equation
Shape of Graph
Linear
y = mx + b
Line
Quadratic
y = ax2 + bx + c
Parabola
Absolute V
Concavity
The graph at the right
represents a portion of
a function f over the
interval x1, x2.
y
o
f
x1
x2
x
Over the mentioned interval, the graph is increasing and bending down when
we analyze it f
Quadratic Functions
Quadratic functions have the following structure.
f ( x ) = ax 2 + bx + c
The formula above is known as the standard form of quadratic functions.
The characteristic term is the one
Graphs of Exponential
Functions
We have already discussed the graph of exponential functions in lesson 3.1.
In this lesson, we will discuss the effect of a and b in the equation y = abx.
Effect of the
THE SINE AND COSINE
FUNCTION
In lesson 6.1, we obtained the graph below.
y
40
o
x
8
16
That shape is new to us. We do not have a formula to model that kind of graph yet.
Because we obtained that shape
Continuous Growth and the
number e
Example 1
Lets consider a savings account where the initial deposit is $1 and the
annual interest rate is 100%.
Find the balance in the account when t = 1 year and i
Comparing Exponential and
Linear functions
Lets analyze how y changes when x increases by 1, for linear functions
For linear function y = 2 + 3x:
If x = 0 y = 2
If x = 1 y = 2 + 3
If x = 2 y = 2 + 3 +
Did you notice any potential limitations including vagueness contradictions, or conflicts in ideas
(which each code and between the two codes)?
I think IEEE Cone of Conduct is a general conduct. It us
Lecture Notes Week 7
Business Writing
During this week, you will begin to read Chapter 12. You should also begin to think
about drafting your cover letter and resume. The purpose for reading Chapter 1
Great exam! Keep up the awesome work!
Problem 1a has a minor error. There is an error in the ordered pair notation for x=4 (-1). Please note
that the ordered pair should read (4,0). The answer you hav
HW set 4.
1.
Forthepiecewisefunction,findthespecifiedfunctionvalue.
Tofindthevalueoff(x)whenx=8,wehavetousef(x)=6xbecause8 1
F(8)=6 (8)=48
2.
The function is decreasing on (- ,1 and increasing on (-1,
GRADE 98/100
COMMENTS: Great exam! Keep up the good work!
Problem 1e has a minor error. The graph you have provided is beautiful, but you have forgotten to label the
equation of the circle on your ske
HW set 2.
1) Write a slope-intercept equation for a line with the given
characteristics.
Passes through (2, -7) and (6, -2)
y 2 y 1
m= x 2x 1 =
5
2(7)
= 4
62
y=mx+b
5
y= 4 x+b. Given point (2,-7)
5
-7
HW set 8
1)Solve.
20
5x
4
=
2
x5
x
x 5 x
2
5 x 4 ( x5 )20
=0
2
x 5 x
2
x 5 x 0
x 0
x 5
5 x2 4 ( x5 )20=0
2
5 x 4 x +2020 =0
x(5x-4)=0
x1=0 (but x 0 )
5x-4=0
5x=4
4
x2= 5
2) Solve
x+6 - 2x = 4
x+6 =
How did mathematicians from the 17th century solve the
following equation?
2 =10
t
The equation above is called Exponential Equation
because the unknown is an exponent.
To solve that equation, mathema
Compound Interest
In the note before Example 2, from lesson 3.4, we concluded that the balance
when the initial amount is A and the annual interest rate is r can be computed
by using
r
B (t ) = A 1 +
INVERSE TRIGONOMETRIC
FUNCTIONS
When computing the sin(40o) the angle 40o is known and the corresponding sine
has to be found.
To find sin(40o) a calculator will use the function y = sin(x), whose out
REFLECTIONS AND
SYMMETRY
Reflections
Lets say that we have the following graph f(x).
y
10
x
f(x)
Lets graph
g(x) = f (x) .
10
y
10
x
10
f(x)
g(x) = f (x)
Lets find
g( 6)
g( 6) = f( 6)
From graph, f( 6
HORIZONTAL STRETCHES
AND COMPRESSIONS
Lets say that we have the following graph f(x).
y
10
x
f(x)
Lets graph
g(x) = f (2x) .
10
y
10
x
10
f(x)
g(x) = f (2x)
Lets find
g( 3)
g( 3) = f ( 2( 3) )
= f ( 6
VERTICAL STRETCHES
AND COMPRESSIONS
Lets say that we have the following graph f(x).
y
10
x
f(x)
Lets graph
g(x) = 2f (x) .
10
y
10
x
10
g(x) = 2 f (x)
f(x)
Lets find
g( 6)
g( 6) = 2f( 6)
From graph, f
VERTICAL AND
HORIZONTAL SHIFTS
Vertical shift
Lets say that we have the following graph f(x).
y
10
x
f(x)
Lets try to graph g(x) = f (x) + 5.
10
y
10
x
10
f(x)
g(x) = f (x) + 5.
Lets find
g( 6)
g( 6)
THE FAMILY OF
QUADRATIC FUNCTIONS
In lesson 2.6, we had a first discussion about quadratic functions.
The following are important aspects of that discussion.
The equation of a quadratic function is
f