Graphing and Beginning Word Problems: Classnotes, G. Battaly

© G. Battaly 2016 1

February 09, 2016

1.1 Graphing

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Study 1.1 CVC 1­9, # 1­ 9; 13, 17, 21, 25; 33 ­ 53; 57, 67 ­ 83

Homework

GOALS: 1. Understand how word problems translate to algebraic equations.2. Determine ordered pairs that are solutions of equations.3. Plot points of solution for an equation and sketch the graph of the equation.

1.1 Graphing

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Convert to Algebra:

The average yearly salary of a an American whose final degree is a master's is $50,000 less than twice that of an American whose final degree is a bachelor's.

Homework

Has the Form:

y is 50000 less than twice x

Graphing and Beginning Word Problems: Classnotes, G. Battaly

© G. Battaly 2016 2

February 09, 2016

1.1 Graphing

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

Has the Form:

y is 50000 less than twice x

___ ____ _____

1.1 Graphing

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

Has the Form:

y is 50000 less than twice x

___ ____ _____

Graphing and Beginning Word Problems: Classnotes, G. Battaly

© G. Battaly 2016 3

February 09, 2016

1.1 Graphing

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Convert to Algebra:

The average yearly salary of a an American whose final degree is a master's is $50,000 less than twice that of an American whose final degree is a bachelor's.

Homework

y = 2x ­ 50,000

where

y = salary of American with master's degree andx = salary of American with bachelor's degree

1.1 Graphing

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

y = 2 x ­ 5When is this sentence true?

Does x = 0 and y = 0 make it true?

Does ( 0, 10) make it true?

Does ( 0, ­5) satisfy the equation, making it true?

Graphing and Beginning Word Problems: Classnotes, G. Battaly

© G. Battaly 2016 4

February 09, 2016

1.1 Graphing

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

y = 2 x ­ 5When is this sentence true?

Does x = 0 and y = 0 make it true?

Does ( 0, 10) make it true?

Does ( 0, ­5) satisfy the equation, making it true?

No(0,0) is not a solution

No(0,10) is not a solution

Yes(0, ­5) is a solution

1.1 Graphing

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

y = 2 x ­ 5When is this sentence true?

Find other solutions to the equation.

x y­3­2­1 0 1 2 3

­5( 1, ___)

( 2, ___)

( 3, ___)

( ­1, ___)

( ­2, ___)

( ­3, ___)

Graphing and Beginning Word Problems: Classnotes, G. Battaly

© G. Battaly 2016 5

February 09, 2016

1.1 Graphing

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

y = 2 x ­ 5

When is this sentence true?Find other solutions to the equation.

( 1, ___)

( 2, ___)

( 3, ___)

( ­1, ___)

( ­2, ___)

( ­3, ___) x y­3­2­1 0 1 2 3

­5

1.1 Graphing

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

y = 2 x ­ 5To Graph the equation,1. Plot the points. 2. Draw curve through points.

x y­3­2­1 0 1 2 3

­11 ­9 ­7 ­5 ­3 ­1 +1

Graphing and Beginning Word Problems: Classnotes, G. Battaly

© G. Battaly 2016 6

February 09, 2016

1.1 Graphing

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

y = 2 x ­ 5To Graph the equation,1. Plot the points. 2. Draw curve through points.

x y­3­2­1 0 1 2 3

­11 ­9 ­7 ­5 ­3 ­1 +1

1.1 Graphing

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

y = x2 ­ 4 x y­3­2­1 0 1 2 3

Graphing and Beginning Word Problems: Classnotes, G. Battaly

© G. Battaly 2016 7

February 09, 2016

1.1 Graphing

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

y = x2 ­ 4 x y­3­2­1 0 1 2 3

+5 0 ­3 ­4 ­3 0 +5

1.1 Graphing

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

y = x2 ­ 4

x y­3­2­1 0 1 2 3

+5 0 ­3 ­4 ­3 0 +5

Graphing and Beginning Word Problems: Classnotes, G. Battaly

© G. Battaly 2016 8

February 09, 2016

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

x y­3­2­1 0 1 2 3

4 4 4 4 4 4 4

Graph:

y = 4

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

x y­3­2­1 0 1 2 3

4 4 4 4 4 4 4

x y­3­2­1 0 1 2 3

2 2 2 2 2 2 2

Graph:

Graphing and Beginning Word Problems: Classnotes, G. Battaly

© G. Battaly 2016 9

February 09, 2016

y = 4

y = 2

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

x y­3­2­1 0 1 2 3

4 4 4 4 4 4 4

x y­3­2­1 0 1 2 3

2 2 2 2 2 2 2

x y­2­2­2­2­2­2­2

­3 ­2 ­1 0 1 2 3

Graph:

y = ­2

y = 2

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

x y­3­2­1 0 1 2 3

4 4 4 4 4 4 4

x y­3­2­1 0 1 2 3

2 2 2 2 2 2 2

x y­3­2­1 0 1 2 3

­2 ­2 ­2 ­2 ­2 ­2 ­2

x y­2­2­2­2­2­2­2

­3 ­2 ­1 0 1 2 3

y = 4

x = ­2Graph:

Graphing and Beginning Word Problems: Classnotes, G. Battaly

© G. Battaly 2016 10

February 09, 2016

y = ­2

y = 2

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

x y­3­2­1 0 1 2 3

4 4 4 4 4 4 4

x y­3­2­1 0 1 2 3

2 2 2 2 2 2 2

x y­3­2­1 0 1 2 3

­2 ­2 ­2 ­2 ­2 ­2 ­2

x y­2­2­2­2­2­2­2

­3 ­2 ­1 0 1 2 3

y = 4

x = ­2Graph:

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

y = | x |

Graphing and Beginning Word Problems: Classnotes, G. Battaly

© G. Battaly 2016 11

February 09, 2016

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

y = | x |

Graphing and Beginning Word Problems: Classnotes, G. Battaly

© G. Battaly 2016 12

February 09, 2016

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

Sketch y = | x | as reference and plot the points that have y values 1 unit below (­1)

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework

Or plot using points