A function is a reliable, predictable rule. If you use the same inputs, you will always get the same outputs. It doesn't matter who does the inputting or what time it is or if it's a holiday or not: each input only produces one output.
It reminds me of this saying*:
It reminds me of this saying*:
* The author of this quote is unknown, but it's usually attributed to Einstein. Because, why not Einstein?
Let's say we have a set of ordered pairs with the same input twice,
connected to two different outputs.
connected to two different outputs.
This could never be a function because it is unpredictable. Inputting 5 creates a "wild card" scenario. What determines whether inputting 5 will give us 19 or 20?
On a graph, we can plot the points (1, 7) (3, 16) (5, 19) (5, 20) and (9, 28) to get a picture of the breakdown:
On a graph, we can plot the points (1, 7) (3, 16) (5, 19) (5, 20) and (9, 28) to get a picture of the breakdown:
As you can see, we can draw a vertical line through both points at the same time. If you can draw a vertical line through two points, you do NOT have a function.
To determine whether something on a graph is a function or not, we use the vertical line test. The vertical line test states that
if you can draw a vertical line
through any part of the curve
and intersect two points,
you do NOT have a function.
through any part of the curve
and intersect two points,
you do NOT have a function.
This is a function:
This is NOT a function:
This is a function:
This is NOT a function:
This is a function:
Notebook:
Classwork & Homework:
1. Create a t-table of inputs and outputs that could be a function.
2. Create a t-table of inputs and outputs that is NOT a function.
2. Create a t-table of inputs and outputs that is NOT a function.