Function Vocab
True or False: A range is the set of possible inputs (x)
False, A range is the set of possible outputs (y)
Evaluate f(x) = -3x if x = 2
f(2) = -6
Given the points, write a function rule:
(0, -2); (1, -1); (2,0)
f(x) = x -2
The point (1, 2) is in this quadrant
Quadrant I
Is it a function?
{(2, 3); (4, 5); (-2, 6)}
Yes, because each input has only one output
The equation that describes a function
A function rule
Evaluate f(x)= 2x + 1 if x= -2
f(-2) = -3
Given the points, write the function rule:
(0, 0); (1, 3); (2, 6)
f(x) = 3x
How do you graph the point (-3, 4)?
Go to the left 3 spaces, and then go up 4 spaces
Using the vertical line test, does the graph of the points (1,3) and (1, 5) represent a function?
No, without graphing, you can see that the inputs are the same but they have two outputs.
The test to tell if a graph is a function
The vertical line test
Evaluate f(x) = -3 -x if x=6
f(6) = -9
(0, 0); (2, 1); (4, 2)
f(x)= 1/2 x
The signs of the points in Quadrant II
x is negative and y is positive
Is this a function?
x | y
2 | 4
1 | 5
2 | 6
No, there are two outputs for a singe input.
Define a function
For each input (x), there is exactly one output (y).
Evaluate f(x) = -(4x+2) if x=7
f(7) = -30
Given the points, write the rule:
(-1, -1); (0, 1); (1, 3); (2, 5)
f(x)= 2x+1
The quadrant that doesn't contain one of these points:
(-2, 3); (3, -4); (2, 3)
Quadrant III
Is a straight horizontal line on a graph a function?
Yes, it passes the vertical line test. It also still has one output for each input
An example of a function in real life is:
A vending machine,
a car,
a phone,
etc
x= -5
Given the points, write the rule:
(0, 5); (1, 6); (2, 7); (-1, 4)
f(x)= x+5
WOOHOO!
Fun question:
How much does a 30- second commercial spot cost for the Super Bowl THIS year?
$7 million
Is a circle on a graph a function?
No, it would not pass the vertical line test.