00:01
In this question, we're asked, what is a function? how do we use function notation to evaluate a function and give an example of evaluating a function with a table, graph, and equation.
00:11
So a function in its most basic definition is a relation which each element of the domain is paired with exactly one element of the range.
00:20
So a function is a relation which each element of the domain is paired with exactly one element of the range.
00:26
And a relation is just a set of ordered pair.
00:28
So for example, if we had the ordered pair, one, two, and two, four, and three, six, this would be a function because the elements of the domain are one, two, and three, and one is only paired with two, two, two is only paired with four, and three is only paired with six.
00:53
If we had the set of order pair 1, 2, 1, 3, and 1, 4, this would not be a function because the elements of the domain are 1.
01:08
1 is the only element of the domain.
01:10
However, 1 is paired with 2, 1 is paired with 3, and 1 is paired with 4.
01:15
So this is not a function in biased definition.
01:19
Another way to think of a function is a rule that takes an input and assigns an output.
01:25
So, for example, if i could write this top function here as a rule, i could say f of x equals 2x, and then i would have to limit where x equals 1, 2, 3.
01:53
Okay.
01:54
And we can see here that the rule is to double the input, right? f of x means to double x.
02:03
So when x is one, i double one and i get two.
02:06
When x is two, i double two and i get four.
02:09
When x is three, i double three and i get six.
02:13
Okay.
02:14
So this is a function.
02:16
This is the bottom one is written in function notation.
02:20
And so if i wanted to show how to use function notation and if i found f of one, so my function says do two times whatever the.
02:30
Input is right and i can see here the input is one so i would do two times one so that would be two so to write an ordered pair for that i would say that this is an input of one and an output of two okay and so you're used to having x and y coordinates x and y coordinates but we could also see this as an x and an f of x coordinate okay, so that's how we can use a table also.
03:08
So if we give a little bit, let's go ahead and plot.
03:15
Let's just define this function, f of x equals 2x.
03:21
So this is a little bit different than this one because this function only had a domain of three values, but if we see f of x equals 2x with no domain limitation, then we can say the domain is all of those.
03:33
Okay, we could make a few table of values.
03:37
For this function where we have x and y or x and f of x okay and we can go into the positive and negatives so we could say negative 2 negative 1 0 1 and 2 and so again the input this is my input here x it just gets 2 times x so whatever x is f of x is 2 times that so negative 2 times 2 would be negative 4 negative 1 times 2 would be negative 2.
04:12
2 times 0 would be 0.
04:14
2 times 1 will be 2.
04:15
2 times 2 be 4...