Warm Up

1) Make two graphs that demonstrate your knowledge of the vertical line test – one of a function and one that is not a function.

2) The length of runway (in feet) needed for a small airplane to land is a function of the speed of the plane (in feet per second). This function can be modeled with the function equation:

R(s) = 0.1s2 – 3s + 22

What type of function is this?

Evalute R (50) - and write a sentence that relates your result to the problem situation.

Using Data to Determine Functions

Algebra One

Data pairs can be plotted on a graph creating a scatter plot.The resulting scatter plot can help

you determine what type of function best models the relationship of the data.

We are going to work with data on our graphing calculators and regression tools to determine the function equation that best models the data.

The path of a diver can be modeled with a function equation.

The diver begins her dive on a diving board 12 feet off the ground. Her distance from the board (x) is noted below for various heights (y) she is in the air during her dive.

X 0 2 3 5 6 8Y 12 15.5 16 14.2 12 8.9

Input the data into your graphing calculator and graph the scatter plot

Looking at the shape suggested by the data points – which function would best describe this data?

Use your calculator to calculate the function equation for your data.

1) Use the function equation to estimate the height for h (7) (Use the Table Function on your calculator – change independent variable to “ask”)*. Write a sentence that relates your answer to the data.

2) Examine your graph – what appears to be the high point of the dive? How many feet is she away from the board when she reaches that high point?

3) Examine your graph – do you see where the diver would reach the water? How far does she appear to be from the board when this happens?

You have just started your own blog. You are keeping track of the number of hits. This table shows the number of hits in each of the first 10 months.

Month 1 2 3 4 5 6 7 8 9 10

hits 22 39 70 126 227 408 735 1322 2380 4285

Input the data in your graphing calculator and create a scatter plot.

Blog Data• What type of function would best

describe this data?

• Use your calculator to calculate the function equation for your data.

• According to your model, how many hits do you expect in your 12th month? f(12)

• How many hits would be in the 34th month. What is wrong with this number?

Heating Costs

The table below shows the average monthly outside temperature and the corresponding average monthly heating cost for a two-story home during the fall and winter of 2008.

Input your data in your graphing calculator and create a scatter plot.

Heating Costs• What type of function would best

describe this data?

• Use your calculator to calculate the function equation for your data.

• According to your model, what do you expect the heating costs to be for f(40)?

• What about f(80)? Does this result make sense?

Car Value – your turn!

The table below shows the value of a car you recently purchased for $35,000. Use your graphing calculator to make a scatter plot and determine which function best models the data.

Year 0 1 2 3 4 5 6

Car Value $

35000 28000 22400 17920 14336 11469 9175

Calculate a function equation – and use it to determine the value of your car in 10 years.

Classwork & Homework

Complete the worksheet on working with data.

**Teacher Notes

• Use the “FINDING FUNCTION EQUATIONS ON YOUR GRAPHING CALCULATOR” handout to instruct students on how to input data on their graphing calculator and then calculate the function equation.

• It is highly recommended that you use the table method to evaluate – it is more accurate than using the rounded equation (which can be extremely significant with exponential & quadratic models).