This piecewise function puzzle is perfect for keeping your students engaged while practicing graphing. There are 6 square puzzles where students will match the piecewise function with a written description and the graph. In this activity, students will cut out puzzle pieces and match the correct answers together.
An answer key is included. Some of the written descriptions give the students the exact equation. Some of the written descriptions describe a general situation and students must match a piecewise function that makes sense.
piecewise functions puzzle answer key gina wilson
See the preview to read the written descriptions of the functions. Make sure this activity is appropriate for your students. Look at the thumbnails and download the preview to see examples of the properties. This activity could be used as an alternative assessment, a partner activity, or as a review before a test. I copy the student's sheet on colored paper and let them hang their finished product in the classroom.
This could also be shrunk when copied and included in an interactive notebook. Piecewise Functions Stations Maze. Function Operations Coloring Worksheet. Look for the green star near the top of any page within my store and click it to become a follower. You will then receive customized email updates about my store.
Answers to Questions on Piecewise Functions
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Piecewise Functions Cut and Paste Puzzle Linear Functions only This cut-out puzzle was created to help students practice graphing a piecewise function along with identifying its domain and range. Students graph each piecewise function the functions are given on a slip of paperidentify the domain and range of each, then cut out the squares and rearrange so the edges meet and paste onto a template. An answer key is included to ensure the graphs are correct The box letters make it easier to grade!
This activity includes only linear functions. For a version with linear, absolute value, and quadratic functions, click here. Licenses are non-transferablemeaning they can not be passed from one teacher to another.
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If most students are at Level 0 or Level 1, then I interrupt them after 5 minutes and ask them as a class if they want a hint. Even if I know they are going to say yes, I take the time to give them the choice. This is a small way of reiterating the fact that it would be possible for them to figure this out themselves, and it also includes them in the decision making process about their learning. Done consistently, this kind of thing creates a very cooperative classroom culture in which students feel that they are agents in the learning process.
If students do want a hint, I write down one part of the function if we think of this as a 6-part function. Then I keep going back and forth with them like this, give them some time to work; if they are struggling I ask if they want a hint; give them a small hint and have them get back to work. This process feels chaotic for teachers who are used to delivering direct instruction in which all the students listen and write stuff down quietly, and it is a sort of chaotic process, because it leaves space for each student to figure stuff out at their own pace.
As long as all students are thinking and talking about the problem, the chaos is fine. A dialogue ensues and this helps me figure out if the whole class or specific small groups need more direction or if they are ready to get started on the assessment, which is the Problem Set.
Once they have showed that they understand the problems in the investigation, I let them get started on the assessment. This is another way that they are the ones setting the pace of their learning. Empty Layer. Home Professional Learning. Professional Learning. Learn more about.
Sign Up Log In. SWBAT write piecewise functions to match given graphs. Big Idea Give students the "answers" and have them write the functions--this reverses the problem from the previous lesson to get students thinking in a different way. Lesson Author.Piecewise functions or piece-wise functions are just what they are named: pieces of different functions sub-functions all on one graph.
Remember that we still use the origin as the reference point for both graphs! See, not so bad, right? Here is the function again:. You can also see that we did this correctly by using the graph above. Sometimes the graphs will contain functions that are non-continuous or discontinuousmeaning that you have to pick up your pencil in the middle of the graph when you are drawing it like a jump!
Continuous functions means that you never have to pick up your pencil if you were to draw them from left to right. And remember that the graphs are true functions only if they pass the Vertical Line Test. We can actually put piecewise functions in the graphing calculator:. Here is what we can put in the calculator:. Here are the keystrokes for using three lines.
Obtaining Equations from Piecewise Function Graphs You may be asked to write a piecewise function, given a graph. To review how to obtain equations from linear graphs, see Obtaining the Equations of a Line, and from quadratics, see Finding a Quadratic Equation from Points or a Graph.
Again, we have to look at each line separately to determine their equations. You might want to review Solving Absolute Value Equations and Inequalities before continuing on to this topic. Make sense? This means we can write this absolute value function as a piecewise function. Here are more examples, with explanations. You might want to review Quadratic Inequalities for the second example below :. So, the piecewise function is:. Try some values less than and great then —2 ; they should work!
You may also be asked to take an absolute value graph and write it as a piecewise function :. We can write this as a piecewise function:. I figured this out by knowing the factors, and taking a good guess! We can see that the parent absolute value function is flipped vertically, move to the left 2and up 1.
This is the same as the piecewise function above. Try it — it works! We learned how about Parent Functions and their Transformations here in the Parent Graphs and Transformations section. We have to start at 0since dogs have to weigh over 0 pounds:. That costs more than a human haircut at least my haircuts! You plan to sell She Love Math t-shirts as a fundraiser.If you're seeing this message, it means we're having trouble loading external resources on our website.
But what we're now going to explore is functions that are defined piece by piece over different intervals and functions like this you'll sometimes view them as a piecewise, or these types of function definitions they might be called a piecewise function definition.
Let's take a look at this graph right over here.How to Find Intercepts of a Piecewise Function
This graph, you can see that the function is constant over this interval, 4x. And then it jumps up in this interval for x, and then it jumps back down for this interval for x. Let's think about how we would write this using our function notation.
Then, let's see, our function f x is going to be equal to, there's three different intervals. So let me give myself some space for the three different intervals. Now this first interval is from, not including -9, and I have this open circle here. Not a closed in circle. So not including -9 but x being greater than -9 and all the way up to and including I could write that as -9 is less than x, less than or equal to That's this interval, and what is the value of the function over this interval?
Well we see, the value of the function is It's a constant -9 over that interval. It's a little confusing because the value of the function is actually also the value of the lower bound on this interval right over here. It's very important to look at this says, -9 is less than x, not less than or equal.
If it was less than or equal, then the function would have been defined at x equals -9, but it's not. We have an open circle right over there. But now let's look at the next interval. The next interval is from -5 is less than x, which is less than or equal to Over that interval, the function is equal to, the function is a constant 6.
It jumps up here.