Identify Input & Output
Mrs. Thomas wants to find out the price charged for the same stereo speaker at different stores
Input: Stereo Speaker
Output: Prices charged for the same stereo speaker at different stores
Input Output
AA 0
BB 1
CC 2
Many-to-many relation
X: -5. -3. -1. 1. 3.
Y: 28. 26. 22. 14. 4.
Not constant rate of change = nonlinear
Decreasing
Five students, Yankel, Eliyahu, Avraham, Moishe, and Dovid have different heights. Their teacher wants to know their heights.
Input: Names of Students
Output: Height of Students
Input Output
0
AA 1
2
One-to-many
The students from the Robotics Club are making mode windmills for a workshop. Each windmill has three blades. The total number of blades needed, y, is a function of the number of windmills they make, x.
y=3x
Increasing and Linear
Yehoshua wants to know what after-school activities each of his friends signed up for so he knows whether he shares the same interests.
Input: Yehoshua's friends
Output: After-school activities
Input Output
AA 0
BB 1
CC 2
One-to-one
Here are a list of points:
(3,1) (2,2) (1,3) (0,4) (2,5) (1,6) (3,7) (2,8)
Draw a mapping diagram to represent the relation, describe what type of relation this is, and tell whether it's a function.
One-to-many
Not a function
A large region has experienced heavy rains. Government officials decide to open a floodgate to release water from the reservoir at a constant rate of 1 cubic kilometer per hour. Before they open the gate, there are 29 cubic kilometers of water in the reservoir. The amount of water in the reservoir, y cubic kilometers, is a function of the number of hours the floodgate has been opened, x hours.
A) Give the least possible input value and the corresponding output value. Tell whether the function is linear or nonlinear. Then tell whether the function is increasing or decreasing.
B) Sketch the graph
A) (0,29)
constant rate of change = linear
Decreasing = Number of hours that the floodgate remains open increases while the amount of water in the reservoir decreases.
A cyclist starts riding from home to another town. His cycling speed, y miles per hour, is a function of the amount of time he takes to cycle, x hours.
X: 1. 2. 3. 4. 6.
Y: 12. 6. 4. 3. 2.
nonlinear and decreasing
The student council orders T-shirts with the school logo from an online company. The cost of each T-shirt is $2, and the shipping charge for all the shirts is $25. The student council wants to find out the total amount of money they pay, y dollars, for the number of T-shirts they order, x.
A) Write an algebraic equation to represent the function
B) Linear or nonlinear
C) Increasing or Decreasing
A) y=25 + 2x
B) Linear
C) Increasing