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Part A: Using Transformations to Graph Linear Functions

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.

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.

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

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

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

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

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

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

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

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

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

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.

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.

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

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/cm3. You look up the density of a block of aluminum at room temperature and find it to be 2.70 g/cm3. 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.

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?

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

Figure 1.4 This table shows the orders of magnitude of length, mass, and time.

Table 1.2

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

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?

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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