Unit 5 HomeworkUnit 5 HomeworkUnit 5 Domain, Range, Function, Introduction to Graphing Sect 1.4—Coordinate Grid HW: pg 28 30-49 all, 53, 54,

Sect 1.5—Patterns, T-Tables, HW: pg 34 8-22 all, 30, 31

Sect 5.1—Function, Domain, Range, Ordered Pairs as Solutions HW: pg 224 13-25 all, 33-36

Sect 5.2—Slope

QUIZ Tuesday, October 25th

Sect 5.4—Slope-Intercept FormSect 5.5—Standard FormSect 5.6—Parallel and Perpendicular LinesUnit 5 Test Friday, November 4th

Section 1.4

Rene Descartes

Born: 31 March 1596 Birthplace: La Haye, France Died: 11 February 1650 (lung trouble) Best Known As: The philosopher who said "I think, therefore I am"

René Descartes is often called the father of modern science. He established a new, clear way of thinking about philosophy and science by rejecting all ideas based on assumptions or emotional beliefs and accepting only those ideas which could be proved by or systematically deduced from direct observation. He took as his philosophical starting point the statement Cogito ergo sum -- "I think, therefore I am."

Descartes made major contributions to modern mathematics, especially in developing the Cartesian coordinate system and advancing the theory of equations.

Section 1.4

Vocabulary:

Quadrantsx-axisy-axisOriginOrdered pairT-TablePlotCartesian Coordinate

Plane

Section 1.4

Graph the ordered pairs, and state if they make a straight line or not.

(1,-3), (2, -6), (3, -9)

(5,2), (7,2), (1,2)

Section 1.4

Directions: Make a table for each equation, and graph the ordered pairs. Connect the points to make a line.

y = 2x + 1

Section 1.4

Directions: Make a table for each equation, and graph the ordered pairs. Connect the points to make a line.

y = ¼ x – 3

Section 1.5

Representing Linear Patterns…writing Linear Equations

X 0 1 2 3 4 5

Y 20 35 50 65 80 95

Step 1: Find the First Difference…meaning, find how much the y value increases for each x.

Step 2: Write a direct relationship y = mx (notice m instead of the letter k)

Step 3: Add the x = 0 value as the constant.

Final linear equation is y = mx + b

Section 1.5

y = 15x + 20

The equation represents a story. The variables both represent something!

To create a T-Table for this equation, you substitute values into the variable x. The variable y will depend on the variable x.

Therefore we call the variable y the dependent variable, and the variable x the independent variable.

Section 1.5

Hrs per month

0 1 2 3 4 5

Total Cost

25 37 49 61 73 85

Find the linear equation

Section 1.5

The prize for a baking contest is $200. If a contestant spends $6 per batch on ingredients to practice a new recipe, write an equation to describe the profit, p, the contestant will make if he wins in terms of the number of practice batches, b, used to perfect the recipe.

Section 5.1

Fancy definition for function:A pairing between to sets of numbers in which each element of the first set is paired with exactly one element of the second set.

Informal definition for function:A unique mapping from one set of numbers (domain…the variable x) to another set of numbers (range…variable y)

x | y x | y 0| 5 0 | 4 1| 7 0 | 6 2| 9 2 | 8

Section 5.1

Math textbooks try to get fancy with showing functions. Here are a lot of common picture representations

x | y 0| 5 1| 7 2| 9

Section 5.1

List the Domain and the Range for the following:

1.{(2,4), (3,5),(4,6),(5,7)}

2.{0,1), (0,3), (0,-5)}

3.{-2, 4),(-1,4),(0,4),(1,4)}

In order for something to NOT be a function, the x-value has to be mapped to two different y values. Which of the above were functions?

Section 5.1

Directions: Complete each ordered pair so that it is a solution to 2x – y = 14

(____, 10)

(____, -7)

(____, -4)

Section 5.2

The steepness of something is called slope. Which “hill” would you rather walk up? Why?

The slope of something is the amount of rise, divided by the run.

Slope: Given two points with coordinates (x1, y1) and (x2, y2), the formula for the slope, m, of the line containing the

points is

Section 5.2

Graph (1,4) and (3, 8). What is the slope between these two points?