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
The starting point when x=0
What is initial value?
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
Slope, rise over run, m
What is constant rate of change?
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)
Any set of ordered pairs
What is relation?
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
No constant rate of change or a curved graph.
What is a nonlinear function?
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
Has a constant rate of change, is a straight line graph.
What is a linear function?