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### Course: Algebra (all content)>Unit 7

Lesson 7: Recognizing functions

# Recognizing functions from verbal description

Checking whether y can be described as a function of x if y is always three more than twice x. Created by Sal Khan.

## Want to join the conversation?

• Why domain is independent & range is dependent?
(9 votes)
• Domain is the set of input values for the function.
Range is the set of output values.
An input value goes into the function, then the function does whatever steps specified by the function to create the output. If you use a different input, then you will likely get a different output (depending upon the function). So, the output is dependent upon what you use for an input value.
Hope this helps.
(25 votes)
• how much money should i donate to khan?
(12 votes)
• However much or little you feel you can give. Thanks for considering donating!
(13 votes)
• How did Sal come up with "if x is 0 then y is 3 if x is 1 then y is 5" i just want to know if its some kind of calculation or trial and error or something. (at )
(10 votes)
• Hi, I do like your question, even I got a question with it,so a function can only have one output, if you want it to be linear function yes that would not work, but he is correct, one input can only have one output, it dose not have to be a constant rate
(10 votes)
• How do you get the equation set up
(7 votes)
• Just get two or three values for x and y that fit the equation and then just extend the graph/line.
(5 votes)
• Is the following is a function?
{0,1,2,3,4,0}
(1 vote)
• You are not really giving enough information here, this is just a set of values I don't know what it is. Now if it was x values or the domain you could see that an x value repeats (0) so it wouldn't be a function.
(12 votes)
• In the above example function, `y = 3 + 2x`, if the `y` was squared, would it no longer be a function? What if there was, in addition to the `y`, also a `y^2`?
(6 votes)
• I still didn't get it, I watched the video like a thousand times. I didn't get the concept!
(3 votes)
• You are a function. You listened to the video (input), you processed it and you responded (output).
You know y = 2x. This means give x a value and y will be double of x e.g. if x = 2,
y = 2 × 2 = 4.
A function is just a different way of expressing this.
Instead of y, we write f(x) which is read f of x (please verify)
So y =2x becomes f(x) = 2x
Input x and get output f(x) which basically says multiply x by 2.
(4 votes)
• What is a function anyway?
(3 votes)
• A function is something that will take an input, and it will do something to that input, to produce an output.

Example y = f(x)

In this example, y is equal to a function applied to x.
(3 votes)
• I dont get that you have the y is doubled like when you said X is 1 so that means Y is 5
(2 votes)
• y is doubled because the problem said that y is equal to three more than TWICE the value of x. The twice part tells us that x has to be multliplied by 2.
y = 3 + 2x
y = 3 + 2( 1 )
y = 3 + 2
y = 5
(5 votes)
• what if there is a strait line in the y and x access is it a function
(1 vote)
• If the graph is a single straight line, then the graph is a function if the line is not exactly vertical, but is not a function if the line is exactly vertical.

Have a blessed, wonderful day!
(3 votes)

## Video 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.