00:01
In this problem, we are going to analyze the graph of our function that we have named f of x.
00:08
Our first question is, what is f of zero? and that means when x is zero, what is y? and in this case, it happens to also be zero, since our graph goes through the origin.
00:20
The next question is when x is six, what is f of x, which means y? so when x is six, y is zero.
00:31
When x is 2 y is negative 2 when x is negative 2 y is 1 is f of 3 positive or negative so if we look at f of 3 right here is our point we can't really tell what that is but we do know since it's below the x axis it would be negative and is f of negative 1 positive or negative so again at negative 1 we're not really sure what that point is, but we know that it's positive.
01:15
Okay, next, for which value of x is f of x equals zero? so when is y zero? and that's going to be at this point, this point, and this point.
01:30
And that is at zero when x is zero, x is four, and x is six.
01:38
The next question says for which value of x is f of x less than zero and f of x is less than zero on this loop down here.
01:51
Now that's between zero and four, but at zero and four we know f of x is zero, so we don't want to include that part.
02:00
So we are going to say f of x is less than zero when x is everything greater than zero, but less than zero.
02:10
Than 4.
02:10
That means between 0 and 4, not including 0 and 4.
02:16
Okay, next, what is the domain of f? the domain of f is say for which values of x is the graph have a part of the graph, and that happens from between negative 4 up to 6, including those two.
02:35
So the domain would be all x's such that x is greater than or equal to negative 4 and less than or equal to 6.
02:48
Okay, range is asking how tall this graph goes and how low.
02:52
So the lowest point on the graph for y is negative 2.
02:55
The highest is 3.
02:57
So our domain, i'm sorry, our range is y is less than or equal to that 6.
03:06
Sorry, i'm looking at range.
03:09
I'm looking at range...