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Linear Equations and Transformations of Graphs, Thesis of Mathematics

Broward CollegeMathematics

Various topics related to linear equations with two variables, including writing equations in slope-intercept form, finding x and y-intercepts, and graphing linear equations. It also explores functions and relations, including finding the domain and range of different functions. Additionally, the document discusses transformations of graphs, including translations, reflections, and dilations. Examples and practice problems for each of these topics, making it a comprehensive resource for students studying linear equations and graph transformations. The level of detail and the range of topics covered suggest this document could be useful for high school or early college-level mathematics courses.

Typology: Thesis

2022/2023

Uploaded on 08/05/2023

jorge-soria-7
jorge-soria-7 🇺🇸

5 documents

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bg1
Linear Equation with Two Variable
A. Write the equation in slope intercept form
B. Find the X and Y intercept
C. Graph
1.
x - y
= 5
2.
2
x -
4
y
= 8
3.
y
= 2
x
+ 1
4.
3
x
+ 2
y
= 7
5.
y
=
-
3
x
+ 2
Write the equation of a line given the following information and graph.
1.
-
4,
-
2;
m
=( ) 3
2
2.
-
3,
-
8
and
4, 6( ) ( )
3.
-
3, 1
and
0,
-
3( ) ( )
4.
3, 2
and
-
4,
-
5( ) ( )
5.
-
2,
-
3
and
-
1, 2( ) ( )
pf3
pf4
pf5

Partial preview of the text

Download Linear Equations and Transformations of Graphs and more Thesis Mathematics in PDF only on Docsity!

Linear Equation with Two Variable

A. Write the equation in slope intercept form

B. Find the X and Y intercept

C. Graph

  1. x - y = 5
  2. 2 x - 4 y = 8
  3. y = 2 x + 1
  4. 3 x + 2 y = 7
  5. y = - 3 x + 2

Write the equation of a line given the following information and graph.

  • 4

m

  1. (- 3 , - 8 ) and ( 4 , 6 )
  2. (- 3 , 1 ) and ( 0 , - 3 )
  3. ( 3 , 2 ) and (- 4 , - 5 )
  4. (- 2 , - 3 ) and (- 1 , 2 )

Functions and Relations

Find the Domain and Range for the following functions

  1. f (x ) =

x + 4

f x ( ) =

x - 2

x - 3

f x ( ) =

x - 2

x + 11 x + 30

2

  1. f (x ) = x + 2
  2. f (x ) = 5 - x
  3. f (x ) =

x

x + 2

  1. f (x ) =

x

x + 2

  1. f (x ) =

4 + x - 2

  1. f (x ) = x + 2 x + 3

2

f x ( ) =

x

x + 16

2

Tranformation of Graphs

Graph the following functions using tranformation. (Hint: create a (x,y) table using the

rules of transformation).

f x

x

2

  1. f (x ) = (x - 2 ) + 4

2

  1. f (x ) = 3 (x - 2 ) + 4

2

f x = -

3 x

2

f x

( ) x

  1. f (x ) = x - 2 + 6
  2. f (x ) = 5 x - 2 + 6
  3. f (x ) = - 5 x - 2 + 6
  4. f (x )= |x - 3 |
  5. f (x )= |x - 3 | + 5
  6. f (x )= 3 |x - 3 | + 5
  7. f (x )= - 5 |x - 3 | + 5
  8. f (x ) = x + 2

3

  1. f (x ) = (x - 3 ) + 2

3

  1. f (x ) = 3 (x - 3 ) + 2

3

f x = -

2 x

3

Symmetry, Even and Odd, Piecewaise Defined Functions

For each of the following functions, state the axis of symmerty and if the function is even or

odd.

1. y = - 2 x + 1

2

2. x = - |y| - 4 3. x + y = 89

2 2

y

x

6 x

2

f x

4 x

3

6. f (x ) = - 8 x - 6 x

5 3

7. f (x )= |x| + 2

x

  • y

2

y

x

2 x

3

x

y

y

3 2