>> Here are a couple of special situations involving linear functions. One of them is a constant function and an example would be F of X is equal to 3. Now we could think of this as Y equals 3 and we know that under that circumstance we have a horizontal line, here is the graph. And we think about it like this, "Gee, if Y equals 3, Y is a vertical distance." So a vertical distance of 3 is associated with every X. There's no X in here to affect anything having to do with X. So for every X the Y value is 3. So for this X, Y is 3. For that X, Y is 3. For that X, Y is 3. For this X, Y is 3. No wonder we have a horizontal line. And under this circumstance, when we start to talk about domain and range and all of those kinds of things that we talked about before, the range is kinda peculiar here. We said before that generally with linear functions the range is all real numbers. Well, with this particular linear function the range is simply 3, Y equals 3, and the slope we is 0. Another linear function of particular note is the identity function, it is F of X equals X or simply Y equals X. And a table of values would reveal that for coordinates, the two components, the two coordinates of every point are going to be identical for--if X is 3 Y is 3, if X is negative 5 Y is negative 5, and so on. So the graph looks like this. This line has a slope of 1 and the Y intercept is at the orgin. Here's another family of functions, the squaring function is the kick starts all of the quadratic functions. It's the most degenerate quadratic function. It would be Y equals X squared. Here's an illustration of the graph. And we can talk about things like domain and range, intercepts and where it's decreasing and increasing, and all of that kind of thing. We can see that the domain would be all real numbers. The range would be, let's see, Y values that are greater than or equal to 0. It looks like here from looking at the graph. And that's the easiest way to identify domain and range I think. The intercepts were both X and Y intercepts are right here at the origin. So the intercepts would be at 0, 0. The function is decreasing and now when you think about decreasing and increasing you think in terms of left to right. But from left to right the graph is decreasing in the interval from negative infinity all the way to 0. And then from 0 to infinity it's increasing. So it decreases and then increases. There's a line of symmetry that appears in this graph. And that line of symmetry is the Y axis here. The minimum point on the graph is at the origin. It's also called the vertex of the parabolic curve. Alright, so we can examine all of these kinds of things involving all of the degenerative forms of these families of functions. Here's the cubic function and notice that--its graph. Now let's talk about some peculiarities in the cubic function. We can talk again about domain and range. The domain all real numbers. The range all real numbers. What about increasing and decreasing? Wow! Well, we're increasing from negative infinity to here. Oh, we're also increasing out here. So the cubic function is increasing throughout its domain. And in terms of symmetry, remember that the idea of symmetry--this function is symmetric with respect to the origin it turns out. Now there's no minimum point here so we don't talk about that. Intercepts now, both the X and Y intercepts are once again at the origin. Here's the square root function. F of X is the square root of X and here is its graph. And once again, domain and range--well, let's see. The domain would be the X values of X that are on the graph would be X values that are greater than or equal to 0. And the range, well again, the Y values that are greater than or equal to 0. So that's domain and range. And we have an increasing graph throughout its domain. From here on out it continues to increase. And we don't have a symmetric quality here. We do have a minimum point and it's at the origin. And the origin also turns out to be the X and Y intercepts.