TODAY IN CALCULUS!…

Note-Taking Tips

Learning Targets : You will represent, classify, and order real

numbers. You will use inequalities to represent sets of real

numbers. You will solve inequalities You will use inequalities to model and solve real-

life problems. Independent practice

NOTE-TAKING TIPS:

• NEATNESS COUNTS!!!

• Start new lessons on new pages.

• Always have a date and headings BIG ANG BOLD to be easy to find.

• You do not have to copy EVERYTHING! But should have example problems to refer to when doing assignments.

• If you do happen to miss something, lessons will be found on the class website.

0.1 INTEGERS AND RATIONAL NUMBERS:

REAL NUMBERS

RATIONAL NUMBERS

INTEGERS

WHOLE NUMBERS

…−√2,−1 ,− 12,0 ,1 ,

34,√3 ,𝜋…

…−1 ,−12,0 ,34,1 ,2 ,…

…−3 ,−2 ,−1 ,0 ,1 ,2 ,3 ,…

0 ,1 ,2 ,3 ,4 ,5…

Incl

udes

pos

itive

and

ne

gativ

e w

hole

nu

mbe

rs

Incl

udes

num

bers

that

can

be

writt

en

as a

frac

tion

IRRATIONAL NUMBERS

Includes numbers that cannot be written as a fraction

All rational and irrational numbers

IMAGINARY NUMBERSA real number multiplied by the term , where

…√−2,5 𝑖 , 𝑖3 ,…

EXAMPLE: Determine whether the real number is rational or irrational.

1. 2.

3. 4.

5.

IRRATIONAL

RATIONAL IRRATIONAL

RATIONAL

RATIONAL

PRACTICE: Determine whether the real number is rational or irrational.

1. 2.

3. 4.

5.

RATIONAL

RATIONAL RATIONAL

IRRATIONAL

IRRATIONAL

OPEN INTERVAL:

CLOSED INTERVAL:

INTERVALS NEITHER OPEN OR CLOSED:

INFINITE INTERVALS:

0.1 ORDER AND INTERVALS ON THE REAL NUMBER LINE(𝒂 ,𝒃)

𝒂 𝒃𝒂<𝒙<𝒃

[𝒂 ,𝒃]

𝒂 𝒃

𝒂≤ 𝒙≤𝒃

¿𝒂 𝒃𝒂<𝒙 ≤𝒃¿

𝒂 𝒃𝒂≤ 𝒙<𝒃

(−∞ ,𝒂)𝒂 𝒃𝒙<𝒂(𝒃 ,∞)𝒂 𝒃𝒙>𝒃

¿𝒂 𝒃𝒙≤ 𝒂

¿𝒂 𝒃𝒙≥𝒃

−∞<𝒙<∞ 𝒂 𝒃 (−∞ ,∞)

0.1 SOLVING A LINEAR INEQUALITYEXAMPLE 1: Solve the inequality and sketch the graph of the solution on the real number line.

1. 2.

Interval notation:( , ) – open intervals[ , ] – closed intervals

¿ ,>¿≤ ,≥

0.1 SOLVING A LINEAR INEQUALITYPRACTICE 1: Solve the inequality and sketch the graph of the solution on the real number line.

1. 2.

5 ∙ ∙5

0.1 SOLVING A LINEAR INEQUALITYEXAMPLE 2: Solve the inequality and sketch the graph of the solution on the real number line.

1. 2.

Multiplying or dividing by a negative number = flip inequalities!

0.1 SOLVING A LINEAR INEQUALITYPRACTICE 2: Solve the inequality and sketch the graph of the solution on the real number line.

1. 2.

Multiplying or dividing by a negative number = flip inequalities!

0.1 SOLVING A POLYNOMIAL INEQUALITY

EXAMPLE 1: Solve the inequality and give the solution in interval notation

Bring all the terms to one side

Factor the polynomial Calculate the zeros

Draw a number line and test theintervals between the zerosto find where the polynomial will be negative

Define the solution set using intervalnotation

𝟑−𝟐 𝟒𝟎−𝟑+¿ +¿−

0.1 SOLVING A POLYNOMIAL INEQUALITY

EXAMPLE 2: Solve the inequality and give the solution in interval notation

Bring all the terms to one side Combine like terms Factor the polynomial Calculate the zeros

Draw a number line and test theintervals between the zerosto find where the polynomial will be negative

Define the solution set using intervalnotation

𝟒𝟏𝟐

𝟓𝟏𝟎+¿ +¿−

0.1 SOLVING A POLYNOMIAL INEQUALITY

EXAMPLE 3: Solve the inequality and give the solution in interval notation

Bring all the terms to one side

Factor the polynomial Calculate the zeros

Draw a number line and test theintervals between the zerosto find where the polynomial will be positive

Define the solution set using intervalnotation

𝟓−𝟐 𝟔𝟎−𝟑+¿ +¿−

0.1 SOLVING A POLYNOMIAL INEQUALITY

PRACTICE: Solve the inequality and give the solution in interval notation

Bring all the terms to one side Factor the polynomial Calculate the zeros

Draw a number line and test theintervals between the zerosto find where the polynomial will be positive

Define the solution set using intervalnotation

𝟒𝟐𝟓𝟑𝟏

+¿ +¿−

0.1 WORD PROBLEMS: PRODUCTION LEVELSEXAMPLES: Use inequality notation to describe the subset of real numbers.1. The estimated daily oil

production p at a refinery is greater than 2 million barrels but less than 2.4 million barrels.

2. The revenue for selling x units of a product is , and the cost of producing x units is . To obtain a profit, the revenue must be greater than the cost. For what values of x will this product make a return profit?

𝟐𝒎𝒊𝒍𝒍𝒊𝒐𝒏<𝒑<𝟐 .𝟒𝒎𝒊𝒍𝒍𝒊𝒐𝒏

Cannot have PART of a unit…

HOMEWORK #1:

Pg.7: 5-35 odd

HEADING ASSIGNMENTS (for your benefit and mine):

• NEATNESS COUNTS!!!

• Head assignments on the upper right hand corner of the paper:Mrs. Un Per.1Date __/__/___HW#1: Pg.75-35odd