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Video transcript
The illustration below shows the graph of y as a function of x. So that's this graph right over here. And then they start to ask us some questions. Complete the sentences based on the graph of the function. So this axis is our y-axis, the vertical axis. Horizontal axis is x-axis. Initially, as x increases-- so let's think about it. Initially, so when we start from x equals 0 and x is increasing, what's happening to y? Well, y is decreasing. So y decreases. So as x increases initially, y decreases. The slope of the graph is equal to blank for all x between x equals 0 and x equals 3. So x equals 0 and x equals 3, what's the slope? Well, every time we move 1 in the x direction, we move down in the y direction. We go negative 1 in the y direction. Move up 1 in the x direction, we go negative 1 in the y direction. So our change in y over our change in x-- our change in y is negative 1 whenever our change in x is 1. So our change in y over our change in x, which is the definition of slope, is negative 1/1. So it's negative 1. And we see that. Every time x increases by 1, y decreases by 1. Starting at x equals 3, y blank as x increases. So starting at x equals 3, y increases as x increases. As x increases, y is increasing. So y increases as x increases. The slope of the graph is equal to blank for x between 3 and 5. So when x increases by 1, y is increasing by 3. So change in y is 3, change in x is 1. Slope is change in y over change in x, which is 3/1. So the slope here is 3. Every time x increases by 1, y increases by 3. For x between x equals 0 and x equals 4, y-- let's see, we can pick less than or equal to, greater than or equal to, or equal. So for x equals 0 and x equals 4, y is less than or equal to 0. So let's do less than or equal to 0. And then they say, for x between x equals 4 and x equals 8-- well, then y is greater than or equal to 0. So let's make sure that we didn't make any careless mistakes here. Let's check our answer. We got it right.