Graphing and Beginning Word Problems: Classnotes, G. Battaly · 1. Understand how word problems...
Transcript of Graphing and Beginning Word Problems: Classnotes, G. Battaly · 1. Understand how word problems...
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
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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