 In this video, we provide the solution to question number 11. For practice exam number 1 for math 1050, we're given the graph of some function f. And we're supposed to identify on what intervals is f increasing. And so how do we identify where it's increasing? Well, when you read a graph, you always read it left to right. We always start from the smallest number in its domain. And we move towards the largest number in the domain. We always read graphs left to right. Now, in that direction, if you're reading it left to right, increasing indicates that the y-coordinate is increasing. Decreasing would mean that the y-coordinate is getting smaller. So as we go from left to right, where are we increasing? Well, if we start over here at x equals negative 6, that's the x-coordinate there, you're at y equals 0. As we progress forward towards x equals negative 4 right here, we'll notice that the y-values are actually getting smaller. So that's not increasing. That's decreasing. So we won't include that. Then as we go from negative 4 to negative 2 right here, we'll notice that the function's getting bigger. That is the y-coordinate's getting bigger. So that's definitely part of it. After negative 2, that was just an x-intercept, it continues to increase coming up here to x equals 0, like so. And so this portion's in green. This would be part of where it's increasing. It's increasing. So what we see here, it's increasing from negative 4 to 0. Now we're gonna put parentheses on it because the function was not increasing at negative 4, because on one side it was going down. On the other side, it was going up type of thing. That's actually what we call a local minimum. It's neither increasing nor decreasing at a minimum. Same thing as the maximum at x equals 0. You'll notice that when we hit x equals 0 though, the function starts to decrease. Again, the y-coordinates are getting smaller until we hit x equals 2. At x equals 2, it then switches a sharp corner, mind you, but it switches, and that starts going up again until we reach x equals 3 right here. So we're gonna throw that into our interval here. It was increasing from 2 to 3, like so. And then you'll notice that for the rest of the graph, as we go from 3 to 6 over here, x equals 6, the function was in fact decreasing again. So we're not gonna worry about that one. So it was decreasing from negative 6 to negative 4 from 0 to 2 and from 3 to 6. We don't want those. We want where it's increasing. So that happened from negative 4 to 0 and from 2 to 3. And it was increasing nowhere else. And so we look for that response amongst the choices and we see that's exactly choice F. So the function was increasing on those intervals right there. And I should point out here that when you're working on these questions of where is the function increasing? Where is the function decreasing? Where is the function concave up? Where is it concave down? We're always referencing the x-coordinates, not the y-coordinates, on which x-address will we be going up? That's what's being asked here. And so the domain, the intervals in the domain that make the function go up is negative 4 to 0 and 2 to 3.