Linear Functions

Brian Nguyen | December, 1 2015 | 3 Period

Linear Functions is FUN!

Table of Contents

  • Definitions
  • Function Notation
  • Interpreting Linear Functions Arising in Applications
  • Analyzing Linear Functions
  • Constructing and Comparing Linear Models
  • Unit Reflection
  • Cited Work

Definitions

Rate- Ratio or fraction
Change- Difference or subtraction

EXAMPLE: 4x-2=2
Slope- Steepness of a line

EXAMPLE: A line going down the graph at 275 degrees
Rate of Change- Change of one quantity over the corresponding change in another.


Y-Intercept- The y value of the point where a line cross the y axis

X- intercept- The x value of the point where a line cross the x axis
Slope Formula- m= (y₂ - y₁)/(x₂ - x₁)
EX: m-(4₂-3₁)(5₂+1₁)

Slope Intercept Formula- y=mx+b Solving for y
EX: y=(4)(3)+2

Standard Formula- Ax+By=C
EX: 4x+5y=38

Point-Slope Formula- y - y₁ = m(x - x₁)
EX: 3 - 3₁ = m(5 - 5₁)

System of Equations/Inequalities

The equations 3x+3y=57 and 4x+2y=58 represents the total balance from the drive through movie in two days. X represents the amount of adults and y represents the amount for children and seniors.

Constraints- x>0 The tickets may not be sold for $0
y>0 The tickets may not be sold for $0
Billy is marketing donuts and cookies to raise money for his books. The donuts costs $2 and the cookies costs $2. She needs at the least $6. She later found out he will need more so he sold his action figures for $4 and he lost $6 he knows he will need to make $12.

Function Notations

This is an example of a function since the (x) input has exactly one (y) output.

And example #2 is not a function since the (x) input doesn't have one (y) output.
Tim was limited in his phone bill for $0.30 for each minute he talked on the phone, and then a flat of $10. The Function would be y=0.30x+10 and the function notation to model the linear function would be f(x)=0.30x+10
Recursive Formula: a(n)=a(n-1)+.3

Interpreting Linear Functions Arising in Applications

Tim worked at his mothers show to save up to buy a video game. For each customer he helps he earns $8. He already has $20 in his wallet, find out how much money he could save with each customer he helps. F(x)=8x+20
y-Intercept=8 The amount if he helps 1 customer.
Slope(Rate of Change)= 8 since he is gaining his money saved.

Analyzing Linear Functions

F(x)=0.7x+8
Tim heard about Bob's job and wanted to be like him. He searched for a job that paid $2, but unlike Bob he had no money to begin with.
COMPARISON
The first example differs because it has a y-intercept of 14 and the other one doesn't. the other difference is that the slope for the first one is much steeper than the other one.

Building Functions

Explicit Formula is a(sub n)=a(sub 1)+d(n-1) ; Plug d (common difference), n (term number), and a(sub 1)(the 1st term) values to find the sequence of the explicit formula.

Explicit- 3,6,9,12 find the 5th term d=3 n=3 a(sub 1)=3 a(sub 3)=3+3(3-1) So, the 5th term is 15

Recursive- 5,10,15,20 find the 5th term d=5 n=5 a(sub 5)=a(sub 5-1)+5 So, the 5th term is 25

Constructing and Comparing Linear Models

Billy and Tim was racing. Since Billy was more in shape, he gave Tim 5 meters head start. If Billy runs 2m per second and Tim runs 1m per second, who will win the 50 m race?
Billy= red
Tim= blue
Big image

Unit Reflection

This unit seemed very complex to me in ways I can not explain. I'm just glad its over. I know I didn't do my full benefits, but I know the next unit might be much better(not promising)

Work Cited