Relations vs Functions
What is a sequence of data points?
A Relation
Linear or Nonlinear?
y = 5x
Linear
What is another word for "rate of change?"
slope
What three things can happen to a line when graphing a model (qualitative graph) of a situation?
Increase, Decrease, Constant
What is my favorite color?
Green
Is this relation a function? How do you know?
(1, 7), (3, 8), (3, 6), (6, 5), (2, 11), (1, 4)
No
Linear or Nonlinear? How do you know?
x | 1 | 2 | 3 | 4
y | 5 | 10 | 15 | 20
Linear - There is a constant rate of change
Write the equation for the linear function with a slope of 5 and a y-intercept of 13.
y=5x+13 or f(x) = 5x+13
A section of a function is called what?
an interval
Classroom Process:
What do you need to do upon entering the classroom?
Quietly begin the warm up.
x | -2 | -1 | 0 | 1 |
----------------------
y | 4 | 1 | 0 | 1 |
Examine the table above. Is the relation a function?
Yes, it is a function.
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
Sketch a qualitative graph showing the temperature inside a house over time as the air conditioning is turned on. Be sure to label your axes.
Temperature decreases over time then levels out at a constant temperature (Graph should not go down to zero)
What is the late policy for middle school work? (How many points are deducted per day late, assuming an assignment is 100 points?)
20% off per day - so 20 points per day on a 100 point assignment
Does the table represent a function? How do you know?
x | y
5 | 3
2 | 2
3 | 5
Yes, Function
Linear or Nonlinear. How do you know?
y=2x3-1
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. Write the linear function that will represent this situation? (Hint: Find the slope and y-intercept)
(1, 2) and (2, 5)
Use y = mx + b
y = 3x - 1
Steve is riding his bike home from school. He stops twice due to traffic, before finally getting home. Sketch a graph of his journey. Be sure the y axis shows the "distance from home" and the x axis shows "time."
decrease, constant, decrease, constant, decrease
What is Mrs. Holland's 2nd favorite subject?
Art
What example did I give when I first introduced Relations and Functions. Explain how the example works, and how it can help you remember the definition of a function.
The elevator and/or the function machine
In a square with side length 's', the perimeter is a ________ function, while area is a __________ function.
Fill in the blank with "linear" and/or "non-linear"
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 the qualitative graph of a runner running around a track 3 times that shows his "distance from the starting line" on the y axis and his running "time" on the x axis.
Increasing, decreasing, increasing, decreasing, increasing, decreasing
What does Mrs. Holland say you should do to prepare for a math test? Be specific!!
Make yourself a practice test and write/solve problems! You can't study for math by looking at the problems, you need to solve them! Use problems in your notebook or on your handouts that you have the correct solutions for.