**Assignment Submission Directions:** Download this assignment sheet and complete by answering all questions. You will need to access the simulations website in order to complete the labs. When completed, save your work and upload the document to the Assignment Upload for graded submission. **50 points**.

Items in red font require submission into a pre populated text box shown as Click here to enter text. (Note: you do not need to fill this one in, for directions purposes only.)

**Part A: Using Transformations to Graph Linear Functions**

Simulation Website: https://phet.colorado.edu/sims/html/graphing-lines/latest/graphing-lines_en.html

**Learning Goals**

- Identify and use a vertical shift to graph a linear function.
- ● Identify and use a vertical stretch or compression to graph a linear function.
- Combine transformations to graph a linear function.

**Activity**

1. Explorethe **slope-intercept** screen for 5 minutes by clicking around the screen and playing with the simulation.

Part 1A: The Parent Function |

2. Check the ‘’ checkbox and play around with the simulation. A linear parent function is the equation. How would you describe the linear parent function,? Cut and paste a screenshot of the parent function and describe the line you see on the screen.

Parent Function Screenshot |

Cut and Paste your screenshot here (just the parent y = x function). |

Describe your linear parent function here. Click here to enter text. |

Part 2A: Changing the b-value |

3. Now, manipulate the equation editor by changing the values in the parent equation:

To write an equation such as y = x + 4; you need to set the fraction to read y = x + 4.This reads as 1 in the numerator and 1 in the denominator.The 4 in this case is the b-value.Use the ‘Save Line’ button after each equation. |

Graph each equation below on the same screen and ‘save line’ after each line. For each function below, indicate the resulting line as it compares to the parent function by selecting the appropriate check box(es).

Function | How is the parent function transformed? Check any that apply. | |

Function A: | [ ☐ ] shifts up [ ☐ ] shifts down [ ☐ ] more steep [ ☐ ] less steep | |

Function B: | [ ☐ ] shifts up [ ☐ ] shifts down [ ☐ ] more steep [ ☐ ] less steep | |

Function C: | [ ☐ ] shifts up [ ☐ ] shifts down [ ☐ ] more steep [ ☐ ] less steep | |

Function D: | [ ☐ ] shifts up [ ☐ ] shifts down [ ☐ ] more steep [ ☐ ] less steep |

Changing the b-value Screenshot |

Functions A-D Transformations Screenshot |

Cut and Paste your screenshot here (with all line equations on one graph). |

4. How does changing the value of ** b** transform the graph of an equation in the form ?

Click here to enter text.

5. Now, hit the ‘Erase Lines’ button to start fresh.

Part 3A: Changing the Slope |

6. Now, manipulate the equation editor by changing the values in the parent equation:

To write an equation such as y = x; you need to set the fraction to read y = x + 0.This reads as 1 in the numerator and 2 in the denominator.A slope of 2 is equivalent to .The 0 in this case is the b-value. Keep your b-value set to zero for this section.Use the ‘Save Line’ button after each equation. |

Graph each equation below on the same screen and ‘save line’ after each line. For each function below, indicate the resulting line as it compares to the parent function by selecting the appropriate check box(es).

Function | How is the parent function transformed? Check any that apply. | |

Function E: | [ ☐ ] shifts up [ ☐ ] shifts down [ ☐ ] more steep [ ☐ ] less steep | |

Function F: | [ ☐ ] shifts up [ ☐ ] shifts down [ ☐ ] more steep [ ☐ ] less steep | |

Function G: | [ ☐ ] shifts up [ ☐ ] shifts down [ ☐ ] more steep [ ☐ ] less steep | |

Function H: | [ ☐ ] shifts up [ ☐ ] shifts down [ ☐ ] more steep [ ☐ ] less steep |

Changing the Slope Screenshot |

Functions E-H Transformations Screenshot |

Cut and Paste your screenshot here (with all line equations on one graph). |

7. How does changing the value of ** m** transform the graph of an equation in the form ?

Click here to enter text.

8. Now, hit the ‘Erase Lines’ button to start fresh.

Part 4A: Determining Line Equations |

9. Now, manipulate the equation editor by changing the values in the parent equation:

To write an equation such as y = x + 3; you need to set the fraction to read y = x + 3.This reads as 1 in the numerator and 2 in the denominator plus 3..A slope of 2 is equivalent to .The 0 in this case is the b-value. Keep your b-value set to zero for this section.Take a screenshot and paste after you plot each of the three equation and enter below. |

Function Screenshot (Positive Slope) |

Function: y = 2x + 5 |

Cut and Paste your screenshot here (with all line equations on one graph). |

Function Screenshot (Negative Slope) |

Function: y = -2x + 5 |

Cut and Paste your screenshot here (with all line equations on one graph). |

Function Screenshot (Positive Slope and Negative b-value) |

Function: y = x -2 |

Cut and Paste your screenshot here (with all line equations on one graph). |

10. How does changing the sign of **slope and b-values **transform the graph of the equation?

Click here to enter text.

Save your work for your files and exit the simulation. End of Part A.

Part B: Estimation Everyday Objects |

11. This drawing is a typical pencil:

WITHOUT using a ruler, estimate how long the pencil is in cm, then in inches. Write your estimate in the table below. (If you do not have a metric ruler, you can print one out using this link.)

Next, measure the pencil. Write your measurements in the table. Finish filling in the table by calculating the accuracy. Find the accuracy by using this equation. Show your calculation in the table.

Pencil Estimate Data Table | ||

Pencil Estimate: | Actual Pencil Measurement: | Accuracy: |

Click here to enter text. cm | Click here to enter text. cm | % Click here to enter text. |

Click here to enter text. inches | Click here to enter text. inches | % Click here to enter text. |

Click here to enter text. meters | Click here to enter text. meters | % Click here to enter text. |

12. What is something in the room that you could estimate the size of that would be close to a few meters (m) in length? Enter your response in the data table.

Object Name: | Estimate (m) | Measurement (m) | Accuracy (%) |

Click here to enter text. | Click here to enter text. | Click here to enter text. | Click here to enter text. |

13. Provide and explain three examples where you have used estimation recently?

Example | Description |

1 | Click here to enter text. |

2 | Click here to enter text. |

3 | Click here to enter text. |

**Conceptual Development Questions**

14. Using the laboratory scenario below, determine what is being computed using the information below.

*Sample Lab Analysis*

In a lab, you are given a block of aluminum. You measure the dimensions of the block and its displacement in a container of a known volume of water. You calculate the density of the block of aluminum to be 2.68 g/cm^{3}. You look up the density of a block of aluminum at room temperature and find it to be 2.70 g/cm^{3}. Next you perform the following analysis:

- Subtract one value from the other: 2.68 – 2.70 = -0.02
- The absolute value of -0.02 or |0.02| is the error.
- Divide the error by the true value: 0.02/2.70 = 0.0074074
- Multiply this value by 100%
- 0.0074074 x 100% = 0.74% (expressed using 2 significant figures)

Describe how the process relates to estimation and which value you have determined by conducting the aluminum density analysis.

Click here to enter text..

15. *Measuring the Circumference of the Earth*

Greek philosopher/scientist Eratosthenes measured the circumference of the earth in the year 240 BC (1732 years before Columbus sailed). His equipment was: a hole in the ground, shadow made by sunlight, and very keen reasoning. His results were amazingly accurate. In his calculations, he used a unit of distance called a stadia. Since no one today is exactly sure how long the stadia is, there is some controversy about how accurate Eratosthenes’s results are.

If we assume that Eratosthenes used the most common unit for stadia, then his measurement for the earth’s

circumference (converted to kilometers) is 46,620 km. An accepted value for the average circumference of the earth is

40,041.47 km. What is the percent difference between Eratosthenes’s measurement and the accepted value?

Click here to enter text.

16. For each of the following scenarios, refer to Figure 1.4 and Table 1.2 to determine which metric prefix on the meter is most appropriate for each of the following scenarios. (a) You want to tabulate the mean distance from the Sun for each planet in the solar system. (b) You want to compare the sizes of some common viruses to design a mechanical filter capable of blocking the pathogenic ones. (c) You want to list the diameters of all the elements on the periodic table. (d) You want to list the distances to all the stars that have now received any radio broadcasts sent from Earth 10 years ago.

Figure 1.4

**F****igure 1.4** This table shows the orders of magnitude of length, mass, and time.

Table 1.2

Prefix | Symbol | Meaning | Prefix | Symbol | Meaning |

yotta- | Y | 1024 | yocto- | y | 10–24 |

zetta- | Z | 1021 | zepto- | z | 10–21 |

exa- | E | 1018 | atto- | a | 10–18 |

peta- | P | 1015 | femto- | f | 10–15 |

tera- | T | 1012 | pico- | p | 10–12 |

giga- | G | 109 | nano- | n | 10–9 |

mega- | M | 106 | micro- | μ | 10–6 |

kilo- | k | 103 | milli- | m | 10–3 |

hecto- | h | 102 | centi- | c | 10–2 |

deka- | da | 101 | deci- | d | 10–1 |

**Table1.2** Metric Prefixes for Powers of 10 and Their Symbols

a) Click here to enter text.

b) Click here to enter text.

c) Click here to enter text.

d) Click here to enter text.

17. (a) What is the relationship between the precision and the uncertainty of a measurement? (b) What is the relationship between the accuracy and the discrepancy of a measurement?

Click here to enter text.

18. Fill in the blank word for the following definition.

Click here to enter text. are reproducible inaccuracies that are consistently in the same direction. These errors are difficult to detect and cannot be analyzed statistically.

19. Fill in the blank word for the following definition.

Click here to enter text. is the degree to which a measured value agrees with an accepted reference value for that measurement.

20. Fill in the blank word for the following definition.

Click here to enter text. is a quantitative measure of how much measured values deviate from one another units.*End of laboratory. Once completed save and upload your work t*

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