 In this video, we provide the solution to question number two for the practice final exam for Math 1050. The graph of a function f is provided here on the screen and we're asked to identify where is this function increasing. Well, notice that if we look at the very left of the graph, there seems to be some type of horizontal asymptote as x goes towards negative infinity. It seems to be approaching y equals one. And so as we move to the left here, we see the graph is getting bigger, bigger, bigger, bigger until it approaches some vertical asymptote at the y-axis. All of that picture, all the left side of the y-axis here is the graph's increasing, so we're not going to include that. So then at x equals zero, there appears to be the y-intercept as y equals one, and then it continues to increase until we hit x equals two. So notice that when x equals two, the function does appear to be decreasing until it hits x equals four, and then after four it continues to decrease until x equals seven. What about the point four itself? It does appear that at the point x equals four, the graph levels off to about a flat level there at that point of inflection where it switched from concave upward to concave downward. And there's some other inflection points, of course, along the way as well. But the significance of the x-intercept four is that the function does level off. So at four, it's neither increasing nor decreasing because the graph is flat, but otherwise from two to seven the function would be decreasing. So that gives us the correct answer. As D, it's decreasing to two to four and four to seven. We exclude four because it level off to have basically a slope of zero at that point.