About this video
Sal explains that y is a function of x only if every input x gives exactly one output y. He then looks at a table where x = 1 gives both y = 1 and y = 2, so y is not a function of x.
You'll be able to
- explain what it means for y to be a function of x.
- check a table to decide whether it represents a function.
- spot an input that maps to more than one output.
Key words
- function
- A rule where every input gives exactly one output.
- input
- The value you put into the function, here x.
- output
- The value the function gives back, here y.
- relationship
- Any pairing of inputs and outputs; not every relationship is a function.
Transcript
In the following table, is y a function of x? In order for y to be a function of x, for any x that we input into our little function box-- so let's say this is y as a function of x. It needs to spit out only one value of y. If it spit out multiple values of y, then it might be a relationship, but it's not going to be a function.
So this is a function. This is a function. If we had a situation where if we input x into a box, it could be multiple possible y's, then this is not a function. So let's think about this table right over here. When x is equal to 1, we get y is equal to 1. But when x is equal to 1 again, all of a sudden, y is equal to 2.
So here we have a situation where we input 1 into our little relationship box, and when we input 1 into our relationship box, we could get a 1, or we could get a 2 for y. So this is definitely not a function. For any input into a function, it has to map to exactly one output.
Here it's mapping to two outputs. So this is not a function.
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