Please give me an Upvote and Resteem if you have found this tutorial helpful. Here's a list of posts created so far on the topic of Functions: However it is not a smooth function since it has a clear edge at x = -1. Thus we have a function that is defined for the domain.Īpplying the conditions, we can plot the piecewise defined function as follows.Ĭreated with: The function shown in Figure 3 is what we call piecewise continuous, since we can draw the entire function without metaphorically lifting the pencil or pen off the sheet. Now, when we overlay the two functions, we have the 2 functions intersecting each other.Ĭreated with: Now, at x = -1, we are told that y = 2 + (-1) = 1 according to the prescribed conditions. Let's have a look at graphing another piecewise defined function. We have one piece ( y = x + 2) to the left of the discontinuity, and we have another piece ( y = x + 2) to the right of the discontinuity. Or y = x + 2 everywhere, except for when x = 2, where we have a point discontinuity.
Graphically, we draw this function as follows.Ĭreated with: And hence, the function can be written or interpreted as. So we have a "hole" in the function at this point.
What is division by 0? Division by 0 in mathematics is undefined, and as such, the function at x = 2 is also undefined. What happens at x = 2? The denominator in the original equation equals 0. So it looks like out chart is going to be a simple straight line, right?. They can be a combination of 2 or more expressions, and those expressions don't even have to be unique.įor example, let's take a look at the function.Īt first glance, it looks like we can simplify this equation as the numerator is the difference of 2 squares. One of the quirky aspects of functions is they don't have to be defined by just a single expression, nor do they have to be continuous.