Name:Mrs. Gorsline Integrated Math 2
Name:Mrs. Gorsline Integrated Math 2
Hour: Unit 1 Guided Notes
Day 1 Homework Notes:
The slope-intercept equation of a line is in the form of ______(p. 141)
The standard form of an equation of a line is ______(p. 157)
3-5 Finding the Equation of a Line
______points determine a ______.
Point-Slope Theorem
______
The equation ______is called the point-slope equation for a line.
Example 2 (p. 163)
Find an equation of the line through (3,5) and (6,-1). Check your work by plugging the point (3,5) into your answer.
Complete p. 165, #2, 5, and 7 (these are preview problems). Show all work
#2#5
#7
Day 1 In Class Notes
There a three ways to write an equation of a line:
Standard FormSlope-Intercept FormPoint-Slope Form
______
______
______
______
Example 1: Supposed you remember that and , but you have forgotten the conversion formula. You know that the formula is linear.
Piece-wise linear functions ______
______
Example 4: During the winter months, an electric company calculates bills for the kilowatt-hours (kwh) its residential customers use based on the following:
$9.00 monthly service fee$.10 per kwh energy charge for the $.07 per kwh energy charge for each first 400 kwh kwh over 400
Draw a graph and figure out the equations for the piece-wise function.
What is a function?
The dependent variable ______on the independent variable. y is usually the ______variable and x is the ______variable. For story problems, always think about which variable depends on the other. Time is almost always ______.
A direct-variation function has the formula ______and ______is the formula for an inverse-variation function. The “k” is a nonzero constant called the ______.
y varies directly as xn or directly proportionaly varies inversly as xn or inversly proportional
Example: The weight w of an adult animal of a given species is known to vary directly with the cube of its height h. Write an equation using w and h and determine the dependent and independent variables.
Day 2 Homework Notes
Order of Operations (PEMDAS) (p. 8)
P 1.
E 2.
MD 3.
AS 4.
Domain and Range (p. 13)
The Domain of a function is ______.
The Range of a function is ______.
Day 2 In Class Notes
Example: Find the domain and range of the following set of points. {(2,8), (6,5), (-3,6), (12,13), (-7,4), (4,6)}
You can also find the domain and range of functions. Often times we use different sets of numbers to describe a domain or range:
Example: Graph the following functions by hand to determine the domain and range:
Day 3 Homework Notes
3.9 Step Functions (p. 186)
The daily charge to park a car at a city lot is $3.00 for the first half hour and $2.50 for each additional hour or portion of an hour. Thus, the cost of parking is a function of time. The table below gives the cost of parking in this lot. Fill in the blanks.
Time (in minutes) / Cost (in Dollars) / Time (in minutes) / Cost (in Dollars)/ 3.00 /
Graph this at the right.
This function is called a ______because it looks like a series of ______.
The ______ is defines as follows:
______
Examples: Evaluate each of the following
Complete p. 189 # 1-7 below. For 1 and 2, refer to the example on the previous page of notes.
Day 3 In Class Notes
Graph the function defined by . To do this in your calculator, type in ______.
x / f(x)Example: A bottling company prepares flavored water. The bottles are packaged in cartons of 8. Write an equation that gives the number of complete cartons c packaged each day if the company prepares b bottles each day.
Day 4 Homework Notes
5-1 Inequalities and Compound Sentences
A mathematical sentence is an ______if it contains one of the symbols below.
Graph the solutions to the following inequalities:
A ______circle means that the number ______in the solution. An ______circle means that the number ______in the solution.
Day 4 In Class Notes
A mathematical sentence in which two clauses are connected by the word ______or by the word _____ is called a ______.
The word ______is the ______of the two sets of solutions. That means that it is the numbers that ______both sets of solutions. We often use the symbol _____.
Example:
A post card must be at least 0.007 inches thick and no more than 0.25 inches thick to be sent in the mail. Write this as an inequality and graph all solutions.
The word _____ is the ______of the two sets of solutions. That means that ______of the numbers in both set of solutions are ______. We often use the symbol ______.
Example:
People who are either younger than 12 or older than 65 pay only half price at the movies. Write this as an inequality and graph all solutions.
Properties of inequalities:
Addition Property of Inequalities
Multiplication Property of Inequalities
Examples:
Solve and graph the solution set.