The worksheets begins with students determining the restrictions on the domain. The student of course can use the technology we used today but they will need to be able to produce a sketch of a piecewise-defined function on their assessment. The worksheet was designed to make sure students are understanding how to graph by hand. Students are given Graphing Piecewise Worksheet. Once we have discussed how to graph students need to try more problems. ![]() I sometimes need to help students determine how to input the inequality for question 4 Students need to use < then = immediately after the < for the application to use the correct notation. To help students focus on the left endpoint, I ask students about the point and ask if there was a point there when you graphed question 2. If a student has not noticed that the graph for questions 2 has no endpoint I make sure return to the student and see how they have completed question 4. I answer questions and make sure that students see know the value of the left endpoint for Questions 2 and 3 is undefined. As students work on this activity I move around the room. I make sure students understand the goal is for them to find a process for graphing piecewise-defined functions by hand. Students are given Writing Piecewise Activity to read over. Today we will use the computer application Desmos Graphing Calculator to see how to graph a function with restrictions on the domain. Prior to this lesson, my students have evaluated and written piecewise-defined functions. Can a function have a point where it is not defined?Īs we finish the discussion I will ask if there is a bigger idea behind this: "What is important when you evaluate a function?" I am hoping students will comment on the importance of analyzing the restrictions on the domain, to make clear where some functions have places where they are undefined.Does -1 agree with the first definition? How about the second part of the graph?.I will have students defend their answers. Others will say there is no answer.Īfter a minute or 2, I will ask student volunteers for answers. Some students will choose a definition to evaluate. I anticipate that there will be some student confusion about what the answer should be. This is also the point where the function changes from one definition to another. The second value, f(-1), gives students a value that is undefined. The first value, f(2), is similar to the problems they worked in previous lessons. Students are given different domain values to evaluate. Hopefully you enjoyed that.Today's Bell Work shows students how a piecewise-defined function may be undefined. Type of function notation, it becomes a lot clearer why function notation is useful even. We have just constructed a piece by piece definition The value of our function? Well you see, the value of And x starts off with -1 less than x, because you have an openĬircle right over here and that's good because X equals -1 is defined up here, all the way to x is Give you the same values so that the function maps, from one input to the same output. If you are in two of these intervals, the intervals should So it's very important that when you input - 5 in here, you know which 5 into the function, this thing would be filled in, and then the function wouldīe defined both places and that's not cool for a function, it wouldn't be a function anymore. Important that this isn't a -5 is less than or equal to. Here, that at x equals -5, for it to be defined only one place. ![]() Over that interval, theįunction is equal to, the function is a constant 6. The next interval isįrom -5 is less than x, which is less than or equal to -1. If it was less than orĮqual, then the function would have been defined at This says, -9 is less than x, not less than or equal. It's a little confusing because the value of the function is actually also the value of the lower bound on this ![]() Over this interval? Well we see, the value That's this interval, and what is the value of the function I could write that as -9 is less than x, less than or equal to -5. X being greater than -9 and all the way up to and including -5. Is from, not including -9, and I have this open circle here. So let me give myself some space for the three different intervals. Then, let's see, our functionį(x) is going to be equal to, there's three different intervals. Over here is the x-axis and this is the y=f(x) axis. Let's think about how we would write this using our function notation. In this interval for x, and then it jumps back downįor this interval for x. This graph, you can see that the function is constant over this interval, 4x. View them as a piecewise, or these types of function definitions they might be called a But what we're now going to explore is functions that areĭefined piece by piece over different intervals By now we're used to seeing functions defined like h(y)=y^2 or f(x)= to the square root of x.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |