F-IF.1.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

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Formative Assessments
Formative Assessments
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Students are asked decide if one variable is a function of the other in the context of a real-world problem.
Cafeteria Function
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Students are shown the graph of a circle and asked to identify a portion of the graph that could be removed so that the remaining portion represents a function.
Circles and Functions
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Students are asked to determine if relations given by tables and mapping diagrams are functions.
Identifying Functions
Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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In this online tool, students input a function to create a graph where the constants, coefficients, and exponents can be adjusted by slider bars. This tool allows students to explore graphs of functions and how adjusting the numbers in the function affect the graph. Using tabs at the top of the page you can also access supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Function Flyer
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This lesson is designed to introduce students to the vertical line test for functions as well as practice plotting points and drawing simple functions. The lesson provides links to discussions and activities related to the vertical line test and functions as well as suggested ways to integrate them into the lesson.
Functions and Vertical Line Test
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Assessment Questions
Assessment Questions
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FSA Sample Question
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Videos of Expert Instruction
Videos of Expert Instruction
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Two sets which are often of primary interest when studying binary relations are the domain and range of the relation.
Domain and Range of Binary Relations
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This video will demonstrate how to determine what is and is not a function.
What is a Function?
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Hook/Performance Tasks
Hook/Performance Tasks
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The purpose of this task to help students think about an expression for a function as built up out of simple operations on the variable and understand the domain in terms of values for which each operation is invalid (e.g., dividing by zero or taking the square root of a negative number).
Domains
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The purpose of this task is to introduce or reinforce the concept of a function, especially in a context where the function is not given by an explicit algebraic representation. Further, the last part of the task emphasizes the significance of one variable being a function of another variable in an immediately relevant real-life context.
The Customers
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This is a simple task touching on two key points of functions. First, there is the idea that not all functions have real numbers as domain and range values. Second, the task addresses the issue of when a function admits an inverse, and the process of ``restricting the domain`` in order to achieve an invertible function.
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