1. Lesson 9–1 Objectives
Be able to translate between various representations of functions
Be able to solve problems using various representations of functions

2. Functions can be represented using:
Verbal description (aka “words”)
Table
Equation – usually in “y=” form
Graph

3. Multiple representations
An amusement park manager estimates daily profits by multiplying the number of tickets sold by 20. This verbal description is useful, but other representations of the function may be more useful.
Multiple representations

4. Example 1  verbal into graph
Sketch a possible graph to represent the following.
1. Ticket sales were good until a massive power outage happened on Saturday that was not repaired until late Sunday.
2. The weather was beautiful on Friday and Saturday, but it rained all day on Sunday and Monday.
3. Only half of the rides were running on Friday and Sunday.

6. Most of the time, any representation can be turned into any of the others
Verbal  equation
Equation  graph

7. Example 2  using one representation to get others
Janet is rowing across an 80-meter-wide river at a rate of 3 meters per second. Create a table, an equation, and a graph of the distance that Janet has remaining before she reaches the other side. When will Janet reach the shore?
Step 1 Create a table.

8. Step 2 Write an equation.
is equal to minus
Distance 80
3 meters per second.
Step 3 use slope and y-intercept to graph the equation.

9. Example 2  using one representation to get others
The table shows the height, in feet, of an arrow in relation to its horizontal distance from the archer. Create a graph, an equation, and a verbal description to represent the height of the arrow with relation to its horizontal distance from the archer.

10. When you want the calculator to PLOT individual points, do the following:
Press “STAT”, then selected “1: Edit…”
Enter “x” values into L1 and “y” values into L2
Press “2ND” “Y=”, select “1: Plot 1”
Choose “on”, the first “type”, Xlist:L1, Ylist:L2, and choose whatever mark you’d like
Finally, go to “ZOOM” and select “9:ZoomStat”

12. Once you know what kind of equation to use (in this case, quadratic), the calculator will find the equation for you:
Press “STAT”, go over to “CALC” and select the regression to do; in this case “5:QuadReg”
Press “ENTER” twice (hint: always use L1 for “x” and L2 for “y”)
There’s your equation…

13. *if you want, type the equation into Y= to see if it matches points

14. Example 3  using multiple representations to solve problems
A hotel manager knows that the number of rooms that guests will rent depends on the price. The hotel’s revenue depends on both the price and the number of rooms rented. The table shows the hotel’s average nightly revenue based on room price. Use a graph and an equation to find the price that the manager should charge in order to maximize his revenue.

16. Example 3  using multiple representations to solve problems
An investor buys a property for $100,000. Experts expect the property to increase in value by about 6% per year. Use a table, a graph and an equation to predict the number of years it will take for the property to be worth more than $150,000.

18. Example 3  using multiple representations to solve problems
Bartolo opened a new sporting goods business and has recorded his business sales each week. To break even, Bartolo needs to sell $48,000 worth of merchandise in a week. Assuming the sales trend continues, use a graph and an equation to find the number of weeks before Bartolo breaks even.

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Lesson Assignment
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