Relations vs Functions
What is a sequence of data points?
A Relation
y = 5x
Linear
In the equation y = 3x + 7, where we are comparing cost, y-variable, and time, x-variable, what does the 3 represent in the situation?
(the units)
cost over time
What three things can happen to a line when graphing a model of a situation?
Increase, Decrease, Constant
Mr. C-ism
What is my favorite whiteboard marker color?
Purple
What kind of realtion is this?
(1, 7), (3, 8), (3, 6), (6, 5), (2, 11), (1, 4)
One-to-Many
Linear or Nonlinear?
x | 1 | 2 | 3 | 4
y | 5 | 10 | 15 | 20
Nonlinear
What variable goes on the x-axis when calculating speed?
(what is speed measured in?)
Time
A section of a function is called what?
an interval
Classroom Process:
Where can you find work from when you are absent?
The class tray
x | -2 | -1 | 0 | 1 |
----------------------
y | 4 | 1 | 0 | 1 |
Relation or Function; what type?
Relation, one-to-many
Linear or Nonlinear
y = 5
Linear
In a situation where a fountain is being filled with water over time, what does the y-intercept represent?
The starting amount of water
Describe the temperature inside a house over time as the air conditioning is turned on.
Temperature decreases
Mr. C-ism:
"I would rather you sacrifice _______ and be accurate then be fast."
(Something I have said about being precise)
Time
Relation or Function, what type?
x | y
5 | 3
2 | 2
3 | 5
Function, one-to-one
Linear or Nonlinear
x = 2
Nonlinear
If Jeff is pedaling at a constant speed, at 1 hour he has travelled 2 miles, after another hour, he has travel 5 miles. What equation will represent this situation?
(y = mx + b)
y = 3x - 1
Steve bikes to his home from school, stopping twice due to traffic, before getting home. Describe a graph of his journey in distance in from his home over time.
decrease, constant, decrease, constant, decrease
Math Time!
What is the only real operation in math?
(we talked about this early in the year)
Addition
What example did I give when I first introduced Relations and Functions
(yes, this is vague, that's why it's worth 500. Think about the grocery store)
The Gumball/Toy Machines
In a square with side length 's', the perimeter is a ________ function, while area is a __________ function.
Linear, Nonlinear
A car moving at a constant speed passes a timing device at t = 0. After 8 seconds, the car has traveled 840 ft. from the device. What linear function in the form y = mx + b represents the distance in ft, 'd', the car has traveled any number of seconds, 't', after passing the timing device?
d = 105t
Describe a graph of a runner running around a track 3 times that tracks his distance from the starting line and his run time.
Increasing, decreasing, increasing, decreasing, increasing, decreasing
I received 2 new things for Christmas from my wife, both of which are in this classroom currently. Any Guesses as to what one of them is?
(Double points if you guess both.)