Relation or Function?
Ordered Pairs:
(-2, 1)
(-2, 5)
(0, -9)
(3, 1)
Is the relation a function?
What is...
No, not a function because the input (-2) has multiple outputs.
Write a function rule for
"the output is four greater than twice the input."
What is...
y = 2x + 4
What two components do you need in order to build a linear function?
What is...
The slope and the y-intercept
Is the function linear or nonlinear?
y = -3(x-1)
What is...
Linear, if simplified you get y = -3x + 3 which is in slope intercept form.
Describe the relationship between the two quantities.
What is..
The speed of wind increases at an increasing rate, then decreases at a constant rate, then increases at an increasing rate and repeats.
What is the difference between a relation and a function?
What is...
A relation pairs an input with an output.
A function is a relation that has exactly one output per input.
Represent the function: y = 5/4x + 3 on a graph
What is..
See Ms. K's white board
Use the table to write a linear function that relates y to x.
X | -1 0 1 2
Y | 3 0 -3 -6
What is..
y = -3x
or
y = -3x + 0
Determine whether the table represents a linear or nonlinear function.
X | -4 -1 2 5
Y | 0 1 2 3
What is...
Linear
x is increasing consistently by 3
y is increasing consistently by 1
Describe the relationship between the two quantities.
What is...
The height of the airplane decreases at an increasing rate then decreases at a decreasing rate.
Is a person's weight a function of their height? Explain
What is...
No, a person's weight is not a function of their height because weight depends on multiple factors beyond just height, such as body composition, genetics, and lifestyle.
What are four ways a function can be represented?
What is...
1. In words
2. A function rule (equation)
3. A graph
4. Mapping diagram/table
Determine y when x=8
y = -2x + 4
What is...
y = -12
Give 3 characteristics of linear functions
What is...
1. forms a straight line that is nonvertical
2. Can be written in slope-intercept form
3. There is a constant rate of change
Sketch a graph that represents the situation
The flu virus spreads quickly at first and then more slowly.
What is...
Is the height of a rocket a function of time? Explain
What is...
Yes, it is a function as its position in the sky changes over time during its flight.
Create an input output table, then graph the function.
For the inputs, use -1, 0, 1
y = 3x + 2
What is...
(-1, -1) , (0, 2) , (1, 5)
Graph the points (-3,10) (0,2)
Then, write a linear function that relates y to x
What is...
y = -8/3x + 2
Find the missing y-value that makes the table represent a linear function.
X | 5 10 15 20
Y | 3 ? 9 12
What is...
The missing y-value is 6.
Sketch a graph that represents the situation.
The sales of a new cell phone increase at an increasing rate, then the sales remain the same, and then the sales decrease at a constant rate.
What is...
What are two ways you can represent a relation?
What is...
Ordered pairs and a mapping diagram
What output is 4 increased by twice the input 3?
What is...
4+2(3) = 10
The table shows the temperature y (in degrees Fahrenheit) at which a tree cricket makes x number of chirps per minute. Write a linear function that relates y to x. Explain the slope and y intercept.
Chirps (x) | 0 20 40 60
Temp (y) |40 45 50 55
What is...
y = 1/4x + 40
The slope 1/4 means that for every 1 additional chirp per minute, the temperature increases by 4 degrees Fahrenheit.
The y-intercept 40 means that when there are 0 chirps per minute, the temperature is 40°F.
Choose the missing y-value that makes the points represent a linear function.
(-3, 9) (-2, ?) (-1,7)
What is..
8
Sketch a graph that represents a situation.
The outside temperature decreases at a decreasing rate and then decreases at a constant rate.
What is...