PowerPoint Presentation

9Today:Warm-UpFunctions, Domain, & RangeVerticle Line Test/MappingInterpreting Graphs

Calculator/Warm-Up Section of NB

Warm-Up: 5 Most Missed from Test 3

5Vers. 1; 39%4

4V.2; 34%10. The final part of your landscaping budget went to building a fish pond and stocking it with lobsters. While shipping the lobsters, 30% of them died. Now you only have 14 lobsters left. How many lobsters did you order?A. 15 B. 20 C. 25 D. 30 E. 40 1. A 32 in. now TV costs $325 after a 13% discount. What was the cost of the TV before the discount? A. $358.76 B. $362.49 C. $367.85 D. $373.56 E. $388.76

3V2 22%2. A 45 in. TV costs $ 550 after a 60% markup. What is the wholesale price of the TV?A. $880.00 B. $220.00 C. $330.00 D. $392.86 E. $343.75

2V.2; 22% 8. For a science project you used 98 toothpicks, or 28% of all the toothpicks you own. How many toothpicks do you have left? A. 350 B. 327 C. 252 D. 197 E. 282

1V.3; 20%9. Your uncle Mario is hired to plant the new flowers and trees. His wage is $6.25/hr. and the planting took 32 hours. What percent of your $8000 budget did you pay Uncle Mario? A) 2.5% B) .25% C) 12% D) 112.5% E) 25%Vocab. Section of NB

Vocabulary ReviewRelation: A set of order pairs.Domain: The x-values in the relation. The set of all first coordinates of the ordered pairs.Range: The y-values in the relation. The set of all second coordinates of the ordered pairs.Function: A relation where each x-value is assigned(maps to) only one y-value.Vertical Line Test: Using a vertical straightedge to see if therelation is a function. Mapping: A diagram used to see if the relation is a function.

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VocabularyThis rule is especially important to remember

The Geometry Theorem:Through any two points in a plane, there can be only one line.(Every equation has only one line, every line has only one equation)Practice Problems:

Breaking Down the GraphThe entire purpose...is to see how something (variable"y") changes when something else (variable "x") changes.

xy

1-1

(0,4)

(4,0)-2Since 'y' only changes when 'x' changes, the y variable is the dependent variable..That is, it depends on x. The x variable is the independent variable. It changes before y does. Looking at the graph above, we see how as x increases, y decreases.

If the x variable represents time,Time

Height/ft.

and the y is height from the groundThe graph, then is showing what?Most likely, the time it takes an object to fall from what height?

Function Rules

Function Rules

Function Rules

The Cost of a Phone CallIT&E charges $0.16/minute for calls to the nation of Mali. Answer the following based on the above information:A. What 2 pieces of data will form our variables?B. Which one is the independent? The dependent?C. Write the equation showing the cost of a call based on the number of minutes.D. Complete a table based on phone calls of 1, 2,3, and 4 minutes of length.E. Write the data for each minute as an ordered pairThe ordered pairs are: (1,16), (2,32), (3,48), (4,64)F. This set of ordered pairs is called a relation and is written in the following way:

y = .16x

The Cost of Renting a BackhoeMary wants to rent a backhoe so she can drive really slow down Middle Rd. Her costs are A. Determine your two variables D. Write the equation (the function rule) showing how y changes when x changes.C. Complete a table based on useage from 0-4 hoursE. Write the data for each hour as an ordered pairThe ordered pairs are: (0,50)(1,70)(2,90)(3,110)(4,130)F. Plot the points on the graph and connect the dots. You have both the line and the equation for that line. Write the equation above the graph.

y =20x + 50$50 rental fee plus $20 per hour.The ProcessB. Which one is the independent? The dependent?Cost, # of hours

What is a Function?A function is a relation that assigns each x-value only one y-value.

What does that mean? It means, in order for the relation to be considered a function, each domain (x) value can point or be associated with only one range (y) value. There are two ways to see if a relation is a function:MappingsVertical Line Test .

Functions: A Short Video

Mapping to Determine a FunctionCreate a mapping of the following relation and state whether or not it is a function.{(-1,2) ; (1, 2) ; (5, 3) ; (6, 8)}

Notice that even though there are two 2s in the range, you only list the 2 once.

-1156

238

This relation is a function because each x-value maps to only one y-value. It is still a function if two x-values go to the same y-value.

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Examples of the Vertical Line Test

functionfunctionNot a functionNot a function.

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Interpreting the Graph

Time (Seconds) Graph 1HeightHeightPeople A. Cost of a laptop, past 10 years B. Drag racing before hitting tree C. World Population, last 700 years D. Person's height during lifetimeE. 3-point shot F. Running up, then down a hill Graph 3Cost Time (Years)

Time (Decades) Graph 2

Speed

Time (Seconds)Speed Time (Seconds)

Time (Years)

Graph 4 Graph 5 Graph 6

Practice1. Identify the domain and range of the following relations: a. {(-4,-1) ; (-2, 2) ; (3, 1) ; (4, 2)}b. {(0,-6) ; (1, 2) ; (7, -4) ; (1, 4)}

3. Graph the following relations and use the vertical line test to see if the relation is a function. Connect the pairs in the given order.a. {(-3,-3) ; (0, 6) ; (3, -3)}b. {(0,6) ; (3, 3) ; (0, 0)}2. Use a mapping to see if the following relations are functions: a. {(-4,-1) ; (-2, 2) ; (3, 1) ; (4, 2)}b. {(0,-6) ; (1, 2) ; (7, -4) ; (1, 4)}

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Answers:

1a. Domain: {-4, -2, 3, 4} Range: {-2, 2, 1}1b. Domain: {0, 1, 7} Range: {-6, 2, -4, 4}3a. 3b.

2a. 2b.

FunctionNot a Function

-4-234-121

017

-62-44

FunctionNot a Function

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Class Work:CW 3.4;Due Today

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