Classwork: Finding Function Values

SOL A1.7e

Name: ______Date: ______

Gizmo Application

You are house-sitting for your uncle. One day you hear a noise from the basement. You walk down the stairs and discover a room filled with strange machines…

Problem A:

1) In the Functions Machine Gizmo:

  • drag Machine A to the blue stand.
  • Above is a row of numbers
  • Click on number 1 to drop it into Machine A.

What happens? ______

2) Click on 2, 3, and 4. What numbers come out?

2: ______3: ______4: ______

3) What do you think will happen if you dropped 10 into Machine A? ______

Explain how you got your answer. ______

______.

4) Test your prediction by running the number 10 through Machine A. Were you correct? ______

5) Write a function rule that represents Machine A. ______

6) Write this rule in function notation: ______

7) Find f(35) algebraically (without the machine).

8) Check your work using the Machine. Were you correct? ______

Activity B

  • Drag Machine B to the left stand.
  • Click on the clipboard in the top right corner of the gizmo.
  • Run numbers through Machine B until you think that you know the function.
  • Record the input and output table below.

Input / Output

What is the function rule? ______

Write this rule in function notation: ______

  • Close the table on your screen and drag one of the machines without a letter on it to the grey stand.
  • Program it with the function rule that you wrote.
  • Drag the machine to the right stand (red)
  • Click on the table clipboard
  • Click on some numbers from your table on the left.
  • Compare the table that you have written down to the one on your screen.
  • Are they the same? ______
  • If so, your function rule is correct! If not, try again to determine the rule for Function Machine B.

Use your function to evaluate the following algebraically.

1) f(12) = ______2) f(-2) = ______3) f(22) = ______

Describe to your uncle the strategies that you used to determine the function rule for Machine B.

______

______

______

______.

Activity C:

Use the strategies that you described to your uncle to determine the function rules for the following tables. Use the programmable function machine to help you figure it out.

Function Rule / Function Notation
Table 1
Table 2
Table 3

Use your function notation to evaluate the following algebraically. Then check your solution with the programmable function machines.

1) Table 1, find f(20)2) Table 2, find f(13)3) Table 3, find f(-4)

Activity D

The city of Metropolis has two taxicab companies: Acme Cabs and Beta Transport. Their prices for different trips are shown in the table below.

1) Based on the table, how do Acme Cabs determine their price?

______

2) How does Beta Transport determine their price?

______

3) Ann wants to go to the Aquarium which is 6 miles away. Which company should she use? Explain.

______

______

______.

Gizmo Activity:

  • Drag machine D onto the left stand
  • Drage Machines A and B onto the right stand, stacked as

shown in the picture to the right.

  • Click through the numbers shown in the input/output tables below- complete the tables as you get your outputs.

1) What is the function rule for Machine D? ______

Function Notation? ______

2) What is the function rule for the combination of Machines A and B? ______

Function Notation? ______

3) Which Machine represents Beta Transport? ______

Activity F

A new cab company has opened. Champion Taxi charges $2 per mile plus a flat fee of $5.

  • Drag a blank machine onto the Function Programmer.

1) What operation do you need to calculate $2 per mile? ______

  • Program the machine to model $2 per mile.

2) What is the function? ______

  • Be sure that SHOW FUNCTION is on and drag the machine to the blue stand on the left.

3) What operation do you need to add $5 to the cost? ______

  • Program a second machine to add in the $5 fee.

4) What is the function? ______

  • Be sure SHOW FUNCTION is on and drag the machine to the left stand BELOW the first machine. THE ORDER IS IMPORTANT.

5) To find the price of a ride in a Champion Taxi, use your machine to complete the table below.

Which variable, distance or price, is your input? ______

Which variable, distance or price is your output? ______

What pattern do you notice in the price? (Hint: how does the price change as the miles change?)

______

______

Based on the pattern, what will be the cost of a 15 mile trip in a Champion Taxi? ______

What is the function that represents the cost of riding in a Champion Taxi? ______

6) Write the functions for each taxi company below. Then determine the cost for each of the following miles.

Taxi Company / Function / Hospital: 6 miles away
Evaluate f(6) / Movie Theater: 8 miles away Evaluatef(8) / McDonalds: 5.5 miles away Evaluate f(5.5)
Acme
Beta
Champion