Archimedes Principle Experiment – Part 3
Given the data set provided to you, complete the following problems. 1. Create a scaBerplot of your data on graph paper. Make sure to label the x and y axis with the correct quanFty and units. Make sure to use an appropriate scale. Create a Ftle for your scaBerplot 2. Create a 3 Column Process Chart. Input your data into the Domain and Range Columns and use the example 3CPC to complete the middle Process Column. 3. What is the equaFon (funcFon rule) governing this relaFonship? 4. Add 6 units to you largest domain value and determine the corresponding range value. JusFfy your answer verbally, by table, by graph, or algebraically. 5. Add 3.7 to you largest range value and determine the corresponding domain value. JusFfy your answer verbally, by table, by graph, or algebraically. 6. Does your data depict a conFnuous relaFonship or a discrete relaFonship? JusFfy your answer. a situaFon that can # texts Discrete: Can you send 0.5 or 0.365 miles ConFnuous: be expressed as a decimal or of text message? No only whole hour fracFon. It is possible to travel texts. A graph of isolated points. month at a speed of 64.24564 mph. 7. Does your data represent an funcFonal relaFonship? JusFfy your answer. 8. Describe the correlaFon depicted by your data. Explain your answer. 9. Determine the Domain and Range of your data. Express the informaFon in the correct notaFon.
Using a 3 Column Process Chart: 1. Input your Domain and Range Values 2. Calculate the change in x values and and the change in y values 3. Determine Rate of Change by placing change in y/change in x 4. Input Slope and Domain values into Process Column 5. Find the y-‐intercept Change in x 3-‐0 = 3 6-‐3 = 3 12-‐6 = 6 15-‐12 = 3
Independent Variable (Units) X0= 0 X1= 3 X2= 6 X3= 12 X4= 15
Finding b: 1. 1.2 (0) + b = 3.7 3 2. 0 + b = 3.7 3. b = 3.7
Process f(x)=mx+b
1.2 (0) + 3.7 3 1.2 = (3) + 3.7 3 1.2 = (6) + 3.7 3 1.2 = (12) + 3.7 3 1.2 = (15) + 3.7 3 =
Dependent Variable (Units) y0= 3.7 y1= 4.9 y2= 6.1 y3= 8.5 y4= 9.7
change _ in _ y Change in y change _ in _ x 1.2 4.9-‐3.7 = 1.2 3 1.2 6.1-‐4.9 = 1.2 3 2.4 1.2 = 8.5-‐6.1 = 2.4 6 3 1.2 9.7-‐8.5 = 1.2 3
= slope = m Set up equaFon to solve for b with (x0,y0) MulFply and simplify SoluFon; value of the y-‐intercept *A similar process can be used for any ordered pair (xn,yn)
FuncFonal RelaFonships x
y
-‐1 5 3
3
-‐1 0
Not a func*on because -‐1 has a y value of 5 and 0
x
-‐1 5 3
3
4
-‐2
CorrelaFons PosiFve CorrelaFon: as x increases, y increases NegaFve CorrelaFon: as x increases, y decreases or as x decreases, y increases No CorrelaFon: neither above, no trend
Domain and Range NotaFon x
y
-‐3
12
-‐1
10
0
9
2
7
5
3
Domain: [-‐3,-‐1,0,2,5] Range: [12,10,9,7,3]
y
These are func*ons since each x value has only one y value, even if the points repeat.
x
y
-‐1 5 -‐1 5 4
-‐2