00:01
All right, in this question, we're going to be looking at two different graphs.
00:03
One of f of x, which is this pink line, and one of g of x, which is this blue line.
00:09
And these are two functions that are graphed, and we're asked about a couple things to learn from this graph.
00:16
So the first one is what is the value of f of negative 4, and also what is the value of g of 3? and so to find this, well, f of negative 4 means x equals negative 4.
00:30
Of 4.
00:30
So we're just going to go over on the left.
00:33
One, two, three, four.
00:35
That's right here.
00:38
And then we're going to see, well, where is this pink line at this x value? and the answer is it's right down here.
00:47
And that is at negative 2.
00:49
So f of negative 4 equals negative 2 at this point right there.
00:54
Then the next one is g of 3.
00:56
For this, we're going to do the same thing.
00:58
We're going to look at where does x equal three? and that is right here.
01:02
We're going to draw a bit of a line and see that this intercepts with the blue line way up there.
01:08
And that is about four.
01:10
And so g of three equals four.
01:14
So now for our next problem, we're asked for what values are both of these f and g equal? and so for this we're going to look at, well, where do the pink and blue lines touch each other? and they are right here and right here.
01:30
So for this answer, we can say f of x equals g of x when x equals this one right here is negative 2, and this one right here is positive 2.
01:50
So we can say x equals negative 2 and positive 2.
01:56
Now for the next problem, we're asked to estimate the solution for when x or when f equals negative 1.
02:03
But real quick, let's erase this graph to make it look cleaner.
02:08
All right, so now we're looking at where does f equal negative 1, or f of x.
02:16
So for this one, we want to draw a line at f equals negative 1, or basically this is the y value.
02:24
And so for this, we're going to draw our line right here at negative 1 and see when does our f, our pink line, intersect with it.
02:31
And that is right here, but also over here.
02:33
So we actually have two solutions.
02:37
So the first one on the left is right here.
02:40
It looks like 1, 2, 3.
02:41
X equals negative 3.
02:43
That's when f intersects with negative 1.
02:46
And then there's another answer, and so we'll include that, and that looks like positive 4 right there.
02:53
So we actually have two answers for this, when x equals negative 3 and positive 4.
02:58
And then for the last, sorry, not the last one, we're next asked for what interval is f decreasing.
03:08
And for this, we want to look at when is f going down when we move to the right.
03:13
And this looks to be starting around here and ending right around here.
03:20
And so this decreasing interval, it starts at zero and ends at four.
03:27
So we can just say that f is decreasing when x is zero...