New! Eight Multiple Choice Domain and Range of Functions Problems
9th - 11th
In this function learning exercise, students determine domains and ranges in eight multiple choice problems. The solutions are provided.
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.
Domain and Range
Here is an excellent, detailed resource that builds on prior work done in Algebra I on domain and range of a function. Learners review the concepts of domain and range, then work in pairs to complete a worksheet of exercises in which they determine domain and range of a relation given its graph and state whether the relation is a function. After discussing their solutions with the class, each pair then selects an item from a grab bag which contains exercises with instructions to sketch possible graphs for a given domain and range. Note that solutions to exercises are not included.
In this college level Pre-Calculus worksheet students evaluate rational functions, identify the domain, vertical asymptotes, and x- and y-intercepts. The three page worksheet contains forty problems. Answers are provided.
In this graphs activity, students solve and complete 15 various types of problems. First, they determine the range of the function of the graph shown and write in interval notation. Then, students find the domain of the function in the graph shown. They also find all three intercepts and state whether the equations represent a line, a parabola, a cubic, a circle, or a hyperbola.
Identifying Graphs of Functions
Match the graph with its function in an exercise that focuses on variations of the graph of y = e^x. Learners are given four graphs on the same set of axes and four functions, all involving e^x. The task is to match each function with its corresponding graph and explain the rationale for each match. An additional focus of this activity is to provide exposure to functions that are used in logistic growth models. The exercise can be used for instruction or assessment.
Domain and Range 2
The short example shown in this video starts with a given a set of numbers in the domain and the range that represent a function. In this example, one needs to simply map the points on a coordinate plane.
Inverse Trig Functions: Arccos
In the third video on inverse trigonometric functions, Sal follows a format similar to the last two. He finds the value for the arcos (-1/2) and shows the restricted domain of the arccos function. He also finds the value for cos(arccos x) and arccos(cos x).
Domain of a Function
We look at a number of different examples of functions and see what their domain is. Sal writes the domain in set notion and shows how different functions can have different input values that cause the function to be undefined.
Area Model of Multiplication Using Base 10 Manipulatives
Explore two-digit multiplication with your class as they work in groups to build models of two-digit multiplication using base 10 manipulatives. They construct rectangles replacing standard numbers with equivalent place values using the blocks, and then relate their rectangles to the traditional written multiplication algorithm.
Functions and Everyday Situations
Use real world scenarios to facilitate discussion of the relationship between variables and how they are represented graphically and analytically. This can work in part as an introduction to functions, as a complete lesson, or as an extension to a unit on the library of functions.
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