Functions
...re: f(x) = x, f(x) = x^2, f(x) = x^3, f(x) = x^(1/2), f(x) = e^x, f(x) = ln(x), f(x) = sin(x), f(x) = cos(x), f(x) = 1/x, and f(x) = |x|. Some functions contain discontinuities. A discontinuity is a value where the function is not defined, on a graph it can be either on the x or y axis. There are several different kinds of discontinuities. First there is the removable discontinuity, or a break in the graph of a function. This is caused by the value of that point is 0/0 and can be removed by factoring, hence the “removable” portion of its name. There is also the jump discontinuity, in which the graph is not defined at an x value and the graph makes a jump on the y axis at that undefined point. Finally, there is the infinite discontinuity, or the asymptote. This discontinuity is caused when a graph infinitely continues on an axis, approaching a point on the other axis but never touching it. There are both vertical and horizontal asymptotes and both may occur in the same graph of a function. My components also have a property called “boundedness” to them. This simply means that if a function has an overall minimum or maximum x value, then it is bounded. If a function has an overall maximum x value, then it is considered bounded above. If a function has an overall minimum x value, then it is considered bounded below. If a function has both, it is considered bounded both above and below, but if it has neither, it is considered unbounded. There are also local minimums and maximums. These are where the graph of a function changes from decreasing to increasing and increasing to decreasing, respectively, and the graph isn’t bounded above for a maximum and below for a minimum or that point isn’t the upper bound for maximum or lower bound for minimum. Also, an interval over which a graph of a function is neither increasing nor decreasing is where the graph is “constant”. F...