Transcript Find the inverse of the function f(x)=3x-5.

Welcome!
Traditional College Algebra
Spring 2013
Class website:
www.math.ksu.edu/math100
Things you need to complete BEFORE next
Thursday, January 24th:
• Purchase your iclicker and register it properly if you already haven’t.
• Download the course syllabus from the class website
• Download the list of course homework problems
• Purchase correct text and TI 83 or TI 84 graphing calculator
• Write down on your calendar/planner the exam dates and FINAL
exam date; there are no make-ups.
• Booking airline tickets to go home on/before MAY 15th is NOT a
reason to reschedule or miss the final. Please re-schedule your
travel plans if you’re planning to leave before or on MAY 15th.
EXAM DATES
•
•
•
•
Tuesday February 5; 7:15pm-8:15pm
Tuesday March 5; 7:15pm-8:15pm
Tuesday April 9; 7:15pm-8:15pm
Wednesday May 15th; (Final Exam) 6:20pm8:10pm
NO MAKEUPS; if there is a documented personal
emergency you must present us with a letter
from the office of student life, then we average
the other two exams for the missed one; you
CANNOT miss the final exam.
EXAMS
• Exam rooms will be posted on our website within 1
week.
• BRING YOUR WILDCAT ID to the examination. THIS IS
MANDATORY
GRADING
• Book homework: 100 points; due Tuesdays at
6pm in the homework cubbies in CW Hall; turn in
according to your recitation instructor.
• ONLINE homework; 100 points; due Tuesdays
at 8AM
• 3 tests; 100 points each
• Final exam 150 points
• Iclicker Correctness – 50 points
• Recitation: 50 points
Homework Guidelines
• In PENCIL
• NO RIPPED EDGES ON PAPER
• Write YOUR NAME; YOUR RECITATION
INSTRUCTOR NAME; Problem #’s, and time of
your recitation class at the top right-hand corner.
• STAPLE.
• Failure to follow these directions will result in a
loss of points.
LATE HW POLICY
• NO LATE HW IS ACCEPTED.
• However, I will drop the lowest 2 book
assignment scores and the lowest 2 online
hw scores at the very end of the semester.
Please do not asked when these will be
dropped, I will remember to drop them!!
• TEST SCORES WILL NOT BE
DROPPED.
GRAPHING CALCULATOR
• TI 83/84 Plus
• TI 85/86 okay
• CANNOT HAVE TI 89/92 or anything with
a QWERTY keyboard or CAS
K-State Online
• You can see how many points you
received on each assignment on K-State
online.
• We take all the curves into account at the
end of the semester; these will not be
shown in KSOL.
Contact Info
• Rekha Natarajan, Coordinator
– [email protected]
– Phone: 532-3023
– Office Hours: Tuesday, 12:30-1:20. And by
appointment.
• Carlos Castillo-Garsow
– [email protected]
– Office Hours: Tuesday/Thursday after class
6
How many numbers do you see?
737
How many numbers do you see?
4
7
How many numbers do you see?
3
7 +2
How many numbers do you see?
3a
7
How many numbers do you see?
One number
One number
6
737
4
7
One number
3
7 +2
One number
3a
7
One number
One number
One number
6
737
4
7
3
7 +2
One number
3a
7
One number
One number
The number is the result of the calculations
Each result has a single place on a number line
The number is the result of the calculations
Each result has a single place on a number line
Type of Numbers
•
•
•
•
•
•
Natural Numbers
1,2,3,4,5,6,…
Whole Numbers 𝕎 0,1,2,3,4,5,6,...
Integers
…-3,-2,-1,0,1,2,3,…
Rational Numbers
any integer/integer
Irrational Numbers 𝕀 any # not rational
Real Numbers
whole number line
(any decimal)
Categorizing numbers
2Î
1.5 Ï
Í
Ë
“2 is an element of N” means 2 is a natural number.
“1.5 is NOT an element of N” means 1.5 is NOT a natural
number.
“N is a subset of Z” means every natural number is also an
integer.
“Z is NOT a subset of N” means there is AT LEAST one integer
that is NOT a natural number (ex: -3)
Which of the following statements is true?
a)
b)
c)
d)
e)
The natural numbers are a subset of the real numbers.
The rational numbers are a subset of the irrational numbers.
The integers are a subset of the natural numbers.
The real numbers are a subset of the rational numbers.
The irrational numbers are a subset of the integers.
Which of the following statements is true?
a)
b)
c)
d)
e)
The natural numbers are a subset of the real numbers.
The rational numbers are a subset of the irrational numbers.
The integers are a subset of the natural numbers.
The real numbers are a subset of the rational numbers.
The irrational numbers are a subset of the integers.
Every natural number has a place on the number line, so
every natural number is a real number.
The natural numbers are a subset of the real numbers.
Interval Notation
3<x≤7
or
(3,7]
All real numbers between 3 and 7
including 7, but not 3.
Interval Notation
x≤4.6
or
(-∞,4.6]
All real numbers less than or
equal to 4.6
Describe the following set using interval notation:
“The set of all real numbers
greater than or equal to 14.”
a)
d)
(, 14] b) [14 , )
(14 , )
c) (14 , 14]
e) None of these
Describe the following set using interval notation:
“The set of all real numbers
greater than or equal to 14.”
a)
d)
(, 14] b) [14 , )
(14 , )
c) (14 , 14]
e) None of these
Distance between two numbers
a-b
Distance between a and b
Distance between two numbers
3- 7
Distance between 3 and 7
3- 7 = -4 = 4
Exponents
• Easiest way:
• an means “multiply a by itself n times”
• Example: 23=2•2•2=8
• This is all you need to know. The rest you
can figure out from this.
Product rule
n
m
n+m
a a =a
•How do I know?
•If I multiply n times and then I multiply m
more times, in total, I’ve multiplied n+m
times.
•Ex: a2a3=(a•a)(a•a•a)=a2+3=(a•a•a•a•a)=a5
Distributive rule of ^ over *
m
m
m
(ab) =a b
• How do I know?
• If I multiply by (ab) m times and then I
multiplied by (a) m times and by (b) m
times.
• Ex: (ab)3=(ab)(ab)(ab)=(aaa)(bbb)=a3b3
Power rule
n
m
nm
(a ) =a
•How do I know?
•If I multiply n times and I do THAT m times.
Then I’ve made m groups of n, or n*m in
total.
•Ex: (a2)3=(a2)(a2)(a2)=(aa)(aa)(aa)=a2•3
=(a•a•a•a•a•a)=a6
0
a =1
•How do I know?
•I don’t. But if I want to keep the product
rule, this has to be true.
•ana0=an+0=an
•ana0=an divide both sides by a
•a0=1
n
-m
m
a =1/a
•How do I know?
•I don’t. But if I want to keep the product
rule, this has to be true.
•ama-m=am-m=a0=1
•ama-m=1 divide both sides by a
•a-m=1/am
m
Last two rules
By using negative exponents
n
a
n -m
n-m
=a a =a
m
a
m
m
æaö
a
ç ÷ = m
èbø
b
Simplify the following, and write your answer using
positive exponents only.
2 3 4
(3a b )
6 -7
6 -7
a) 12a b
b) 9a b
c) 81a
8
81
a
d)
12
b
b7
8
e) None of the above
Solution by rules
2 -3 4
(3a b )
-3 4
= 3 (a ) (b )
4
2 4
2·4 -3·4
= 81a b
8 -12
= 81a b
81a
= 12
b
8
D
Solution by counting
2 -3 4
(3a b )
2 -3
2 -3
2 -3
2 -3
= (3a b )(3a b )(3a b )(3a b )
3aa 3aa 3aa 3aa
=(
)(
)(
)(
)
bbb bbb bbb bbb
4 8
3 a
= 12
b
D