About this video
Sal turns the sentence 'the value of y is always 3 more than twice x' into y = 3 + 2x. Because each input x gives exactly one y (for example x = 0 gives 3 and x = 1 gives 5), y is a function of x.
You'll be able to
- write an equation from a verbal description like '3 more than twice x'.
- decide whether a verbal rule makes y a function of x.
- explain that two inputs may share an output, but one input can't have two outputs.
Key words
- function
- A rule where every input gives exactly one output.
- twice
- Two times a number, so twice x is 2x.
- input
- The value you put into the rule, here x.
- output
- The value the rule gives back, here y.
Transcript
The value of y is always 3 more than twice x. So we can say that y is equal to 3 more than twice x. So it's 3 plus 2x is another way of saying this first sentence. So is y a function of x? So whenever you're asked whether something is a function of something else, you're really just saying, look, for any input x, does it map to exactly one y?
So if we say y is a function of x, in order for this to be a function for any x that you input into this function, you must get exactly one y. So if you input an x you must get exactly one y value. If you got two values, then it's no longer a function. For any input, you get exactly one y.
You could have two inputs that get to the same y, but you can't have one input that results in two different outputs. You don't know what the function is valued at at that input. Now, here it looks pretty clear that for any input, you get exactly one output. Any input uniquely determines which y.
It's not like if you put an x in here, you're not sure what y is going to be. You know what y is going to be. If x is 0, y is 3. If x is 1, y is 5. And so this is definitely a function of x. y is definitely a function of x.
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