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### Course: 8th grade > Unit 3

Lesson 12: Recognizing functions- Testing if a relationship is a function
- Relations and functions
- Recognizing functions from graph
- Checking if a table represents a function
- Recognize functions from tables
- Recognizing functions from table
- Checking if an equation represents a function
- Does a vertical line represent a function?
- Recognize functions from graphs
- Recognizing functions from verbal description
- Recognizing functions from verbal description word problems

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# Checking if a table represents a function

Sal determines if y is a function of x from looking at a table. Created by Sal Khan.

## Want to join the conversation?

- If there is the same output for two different inputs, then is it still a function?(17 votes)
- Yes, that qualifies. As long as each input yields only one output. It makes no difference whether the output is unique.(13 votes)

- so, I'm learning functions in my high school algebra 1 class, and i'm still a bit confused. Can you explain how to solve a function?(4 votes)
- To solve a function, you need to understand the mechanism. A function is like a microwave, you put something in it, and something will come out. So, an input and an output. For example f(x) = x + 1, given x is 7. You would insert 7 into the equation, f(7) = 7 + 1, which is 8. So the input is 7, resulting in an output of 8. Also, the f(x) part does not mean mulitplication, it is a format used for functions. Good luck!(7 votes)

- can a swiggly line be a function(5 votes)
- Yes, but only if it doesn't have the same x-value twice(5 votes)

- i dont get this pleas help(2 votes)
- if x corresponds to 2 y values it is not a function . if x corresponds to 1 y value then it is a function(8 votes)

- Hi! I'm having a lot of trouble with a specific question regarding functions, but I'm not sure where to post it.. the question is, if f(x) |-> ax^2 + bx + c, and {x: 3, 1, -2} and {y: 32, 6, -3} then what are the values of a, b and c? So far I have done this using the quadratic formula as well as by using simultaneous equations. Does anyone else have a better idea on how to do it?(3 votes)
- Write 3 equations by plugging in each x and y:

9a + 3b + c = 32

a + b + c = 6

4a - 2b +c = -3

At this point is is just a straight solve of 3 linear equations with 3 unknowns, so just use your preferred technique to solve for a, b, and c.(3 votes)

- What if we had a table and a point repeated? For example, *(1,1)* and then, it is *(1,1)* again. Would that be a function or not?(3 votes)
- yes it would still be a function because if you input 1 and get only 1 then it is considered a function(3 votes)

- Is not a function continuous ?

Isnt't is a series ?(3 votes)- I dont know how to awnsore this for you but what I can tell you is that it does not go on forever(3 votes)

- but what if you have like, 1,1 and 1,2. what do you do? i'm confused at0:15. what do you do?(3 votes)
- hello unknown person

I will tell you that you cant do anything because the relation is not a function so if you have (1,1) and (1,2) it is then considered not a function

hope this helps

the master(3 votes)

- How do I work a table that has variables in place of the x-values?(3 votes)
- can different inputs have the same output??(1 vote)
- Sometimes yes. For example, consider y=0x. If x = 1, y = 0. If x = 2, y is still 0.(5 votes)

## Video 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.