3.6.1 Building Functions from Context ( MMC9-12.F.BF.1a)

1. 3.6.1 Building Functions from Context (MMC9-12.F.BF.1a)

2. For each situation, write a function which models the given information and use it to answer the questions. Ex. 1. The starting balance of Anna’s account is $1250. She takes out $30 each month. How much money is in her account after months 1, 2, and 3?

3. Ex. 1. The starting balance of Anna’s account is $1250. She takes out $30 each month. How much money is in her account after months 1, 2, and 3? Use the given information to fill in the table. Determine if there is a common difference or a common ratio.

4. Recall that arithmetic sequences are linear, so use the slope-intercept form: We know the y-intercept: ___________ We know the slope(rate of change)________________ So the equation is ________________

5. Use the given information to fill in the table. Determine if there is a common difference or a common ratio.

6. Recall that geometric sequences are exponential, so use the explicit form: We know : ___________ We know the common ratio:____________ So the equation is ________________

7. Ex 3. A video arcade charges an entrance fee of $5, and an additional $1 per game. Find the total cost for playing 0, 1, 2, or 3 games. b. Write the function that represents the cost as a function of games played. _________________ c. What is the domain of this function? ___________ d. Is it discrete or continuous?__________

8. 3.6.2 Building Functions from Graphs and Tables (MMC9-12.F.LE.2)

9. The following graphs will help you to determine a function when you are given its graph: Exponential functions Ex. :

10. Ex.

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12. Ex.

13. Recall that linear functions correspond to arithmetic sequences which have a commondifference. The common difference corresponds to the slope. Linear: where m is the common difference and b is the y-intercept.

14. Similarly, exponential functions correspond to geometric sequences which have a common ratio. This will help you write the function when given a table. Exponential: where b is the common ratio and a is the y-intercept.

15. Ex. 1 Determine the equation that is graphed: Step 1: linear or exponential? Step 2: Find 3 points on the graph whose x-coordinates are consecutive integers. Step 3:If the graph is exponential, find the common ratio. Step 4: Use the y-intercept and common ratio to write the equation.

16. Ex. 2. Determine the equation graphed: Step 1: linear or exponential? Step 2: Find the y-intercept. Step 3: If the graph is linear, find the slope. Step 4: Use the y-intercept and slope (common difference) to write the equation.

17. Ex. 3. A clothing store discounts items on a regular schedule. Each week, the price of an item is reduced. The prices for one item are given in the table. Week 0 shows the starting price of the item. Determine if the relationship is linear or exponential, then write the function that relates the week and the price.

18. Determine if there is a common difference or a common ratio.

19. Determine if there is a common difference or a common ratio. Use the y-intercept and the common ratio to write the equation:

20. Problem-Based Task 3.6.2 Julia is studying the sum of interior angles in polygons. She creates polygons with 3, 5, 6, 7, and 9 sides, and records the sum of the interior angles in each polygon in a table. Find a function that models the relationship between the number of sides in a polygon and the sum of the interior angles. Determine if there is a common difference or a common ratio.

21. Substitute the common difference for m in y=mx+b. Find the y-intercept by substituting an ordered pair for x and y and solving for b. Use the information to write the equation: