F-BF.2.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them

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Formative Assessments
Formative Assessments
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Students are asked to use technology to graph exponential functions and then to describe the effect on the graph of changing the parameters of the function.
Comparing Functions – Exponential
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Students are asked to compare the graphs of four different linear functions to the graph of f(x) = x.
Comparing Functions – Linear
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Students are given the graph of f(x) = x2 and are asked to compare the graphs of five other quadratic functions to the graph of f.
Comparing Functions – Quadratic
Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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Using this virtual manipulative, students are able to graph a function and a set of ordered pairs on the same coordinate plane. The constants, coefficients, and exponents can be adjusted using slider bars, so the student can explore the affect on the graph as the function parameters are changed. Students can also examine the deviation of the data from the function. This activity includes 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.
Data Flyer
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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 is a graphing tool/activity for students to deepen their understanding of polynomial functions and their corresponding graphs. This tool is to be used in conjunction with a full lesson on graphing polynomial functions; it can be used either before an in depth lesson to prompt students to make inferences and connections between the coefficients in polynomial functions and their corresponding graphs, or as a practice tool after a lesson in graphing the polynomial functions.
Function Matching
Assessment Questions
Assessment Questions
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Videos of Expert Instruction
Videos of Expert Instruction
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How many steps will he run on the super stairs? How long will it take him to run them?
Super Stairs
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Hook/Performance Tasks
Hook/Performance Tasks
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The task addresses the first part of standard MAFS.912.F-BF.2.3: ``Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative).``
Medieval Archer
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This problem solving task examines, in a graphical setting, the impact of adding a scalar, multiplying by a scalar, and making a linear substitution of variables on the graph of the function f. This resource also includes standards alignment commentary and annotated solutions.
Transforming the graph of a function
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This task aims for students to understand the quadratic formula in a geometric way in terms of the graph of a quadratic function.
Building a quadratic function from f(x) = x^2