Piecewise Functions Teacher Resources
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Making Piecewise Functions Continuous and Differentiable
Young scholars explore the concept of piecewise functions. In this piecewise functions lesson plan, students discuss how to make a piecewise function continuous and differentiable. Young scholars use their Ti-89 to find the limit of the function as it approaches a given x value. Students find the derivative of piecewise functions.
Linear Piecewise Functions
Students explore the concept of piecewise functions. In this piecewise functions lesson plan, students graph piecewise functions by hand and find the domain and range. Students make tables of values given a piecewise function. Students write piecewise functions given a graph.
Introduction to Piecewise Functions
Investigate and discuss piecewise functions. Using TI-nspire, examine peicewise functions through an analysis of functions and their respective domains. Included are teacher and student documents.
Writing Formulas for Piecewise Functions
Pupils explore piecewise functions. In this Algebra II/Pre-calculus lesson, students write formulas for piecewise functions and check their work on the calculator. The lesson assumes that pupils have seen piecewise functions prior to this activity.
Swet and sour with a hat
Eleventh graders explore the TI-InterAcitve!. In this Algebra II lesson, 11th graders examine features of the TI-InterActive! including drawing on a Graph, using Stat Plots, exploring the syntax for piecewise functions, and using sliders in order to obtain parametric variations. The lesson is designed to encourage students’ creativity.
Piecewise Functions, Continuity, and Differentiability
Learners explore the concept of piecewise functions. In this piecewise functions lesson, students find the derivatives of piecewise functions. Learners determine points of discontinuity and jumps in the graph using their Ti-89 calculator.
Choosing a Cell Phone Plan
Here is an activity that should catch the attention of your class! It focuses on the real-world problem of selecting the best cellular phone plan. This exercise would be especially good to use when introducing piecewise functions. Learners compare costs for various data plans, considering such features as unlimited talk and unlimited texts, to determine which plan is the most cost effective for different scenarios. The task requires giving graphical and numerical representations of the options and writing a justification for choosing a particular plan. The resource includes a detailed commentary for the teacher and three follow-up questions.
Writing Formulas for Piecewise Functions
High schoolers explore the concept of piecewise functions. In this piecewise functions lesson, students write functions to represent the piecewise function graphs on their Ti-Nspire calculator. High schoolers determine the formula given the piecewise function graph.
Is There a Limit to Which Side You Can Take?
Calculus high schoolers find the limit of piecewise functions at a value. They find the limit of piecewise functions as x approaches a given value. They find the limit of linear, quadratic, exponential, and trigonometric piecewise functions.
Slope, Vectors, and Wind Pressure
A hands-on lesson using the TI-CBR Motion Detector to provide information to graph and analyze. The class uses this information to calculate the slope of motion graphs and differentiate scalar and vector quantities. There is a real-world activity of a Roof Manufacturer's Test in regards to the pitch of roofs, as well as several other real-world scenarios.
Learners investigate how to use piecewise functions to describe various situations in everyday life. They explore scenarios such as the intensity of workout routines, the rise and decline of reported cases of malaria, and the varying rate of two hikers on a camping trail. Tasks include writing and graphing a piecewise function to describe a situation, writing a piecewise function when given the function's graph, and interpreting information about the graph of a piecewise function in the context of the problem.
Eighth graders, after researching the properties of graphs of conic sections, absolute value and inverse relations, make a drawing of precise functions and relations from a specified list of equations. The final design should analyze the domains needed for the equations. In addition, they explain completely what was done and why it was done.
NUMB3RS Activity: Seeing in the Dark
Students investigate sonar technology. In this Algebra II lesson plan, students explore use sound waves to measure distance. The students conduct several experiments with a CBR 2 unit to collect data and graph distance vs. time. Students model the data with piecewise functions.
NEXT GENERATION SPACECRAFT-Orion
Students investigate the volume of a solid. In this calculus lesson, students use integration to find the volume of a solid generated by a region, the Orion crew module.
Students investigate semiconductor chips and its technological use. In this algebra lesson, students use the semiconductor chip as a real life application tool to study functions, linear equations and quadratic equations. They relate the growth in technology because of the conductor chip to exponential functions.
Solar Flare Reconstruction
For this solar flare reconstruction worksheet, students read about the 'saturation' point of satellite detectors when solar flares are at their most intense phase of brightness. Students are given x-ray flare data and they re-plot the data to estimate the peak of intensity. They create 2 exponential functions to fit the data and estimate the peak intensity and time. Students use calculus to integrate one of the functions and calculate the total energy radiated by the flare.
Piecewise Defined Functions
Graph piecewise functions as your learners work to identify the different values that will make a piecewise function a true statement. They identify function notations and graph basic polynomial functions. This lesson includes a series of critical thinking questions and vocabulary.
Let's Get Physical
Students collect data using the CBL. In this statistics lesson, students predict the type of graph that will be created based on the type of activity the person does. The graph represents heart rate depending the level of activity.
Exciting Sack Race: An Introduction to Algebra
Students discover piecewise functions and analyze slope. In this algebra lesson, students explore slopes through stories and motion based scenario. This activity leads up to constraints being put on the function.
Students investigate piecewise functions. In this algebra lesson, students model piecewise functions in the real world. They graph the parts of the functions following the restrictions of the domain.