CK-12 Foundation
Vertical Translations
Change the y-intercept by adding a constant to the function. Individuals move three functions vertically along the y-axis. As they observe how the equation of the functions change with the vertical movement, learners determine how to...
CK-12 Foundation
Vertical Translations: Vertical Shift of Sinusoidal Functions
Create a shift in TV viewing habits. The interactive presents a cosine model of an individual's TV viewing habits during a year. Class members move the model to reflect given conditions. Finally, they determine key features from the...
Curated OER
Trigonometric Graphs: Vertical Shift and Stretching
In this trigonometric graph instructional activity students describe the period, amplitude and vertical shift of given functions. They graph the trigonometric function. This four-page instructional activity contains 16 multi-step problems.
CK-12 Foundation
Horizontal Translations or Phase Shifts: Tangent
Patterns can be shifty! Find the pattern when shifting the graph of tangent. Pupils move the graph of tangent to different locations on the coordinate plane. They observe what happens to the function and its vertical asymptotes before...
CK-12 Foundation
Horizontal Translations or Phase Shifts: Cosine
If cosine is shifted, how is its equation affected? Learners manipulate the graph of cosine by moving the y-intercept to different locations on the coordinate plane. Pupils determine the new equation that models the shifts.
CK-12 Foundation
Horizontal Translations or Phase Shifts: Sine
Shift a trigonometric function and find its new equation. Pupils translate a sine function on a graph. The scholars determine the equation of the function that represents the translated graph and observe the connection between a...
CK-12 Foundation
Horizontal Translations or Phase Shifts: Horizontal and Vertical Translations
It is all about the shift. Pupils translate the graph of a cubic function to different marked locations on the plane and determine the new equation that represents the shifts. The activity is designed to encourage individuals begin to...
West Contra Costa Unified School District
Shifting Linear Equations in Function Notation
Time for a shift in thinking! Learners examine translations of linear functions. They use function notation to describe the translation and make connections to the graph.
Curated OER
Trigonometric Graphs: Vertical and Horizontal Shift of Functions
In this vertical and horizontal shift of functions, students describe the period, amplitude, horizontal shift and vertical shift of each given function. This three-page worksheet contains seven multi-step problems.
CK-12 Foundation
Analyzing the Graphs of Functions: Analyzing a Rational Function
Shift the function and transform the key features of the graph. By translating the graph of the rational function, class members find out how the key features alter. Pupils determine the domain, range, asymptotes, and intervals of...
Curated OER
Trigonometric Graphs
In this trigonometric graphs worksheet, 11th graders solve and complete 16 different problems. First, they determine the period of the given functions. Then, students describe the period, amplitude, and vertical shift of each function....
Curated OER
Building a Quadratic Function Form
Comparing the movement of graphs geometrically when small changes are made to the parent function motivates this collaborative discussion on the transformations of functions to their various forms. Vertical and horizontal shifts due to...
Curated OER
MT-A141 PreCalculus: Worksheet 6.4
In this precalculus learning exercise, students predict the graph of given functions and draw conclusions about each one. Students define a transformation, and determine the amplitude, period, phase shift and vertical shift of given...
Curated OER
Modeling With Circular Functions
Students explore circular functions. They identify the amplitude, period, phase shift and vertical shift of circular functions. Students analyze phenomena described by sine waves and they find mathematical models for transforming images...
Modesto Junior College
Graphical Transformations of Functions
Transform your knowledge from average to excellent with this comprehensive guide to function transformations. All of the types of shifts, stretches, and reflections are included with an explanation and coordinating graph to show...
Alabama Learning Exchange
Technology for Displaying Trigonometric Graph Behavior: Sine and Cosine
Students explore the concept of sine and cosine. In this sine and cosine lesson, students work in groups to graph sine and cosine functions. Students examine how coefficients in various parts of each parent function shift the graph. ...
EngageNY
Four Interesting Transformations of Functions (Part 2)
What happens to a function whose graph is translated horizontally? Groups find out as they investigate the effects of addition and subtraction within a function. This nineteenth instructional activity in a 26-part series focuses on...
Curated OER
Let's Play Some Ball!
Pupils review horizontal and vertical shifts of a parabola and how they effect a specific quadratic formula. They play a basketball review game in which they try to find the right quadratic equation for a given problem in order to earn...
Curated OER
Related Functions
In this function learning exercise, students discuss how a function would change if it shifted on a graph. They create ten new, related functions. Students identify odd, even and symmetric functions. This two-page learning exercise...
Curated OER
Vertical and Horizontal Translations
Eleventh graders study seven functions. They use their handheld calculator to determine which family of functions the equation belongs, the parent function described, and they calculate the vertical and horizontal translation.
Curated OER
Upward and Downward Motion of Melody
First graders explore the notion of upward and downward melody motion. They hum, sing, and listen as the melody moves up and down. To show what they know, they put their thumbs up or down as the melody shifts.
PBS
Toothpicks and Transformations
High schoolers investigate quadratic functions using geometric toothpick designs. They review transformations of quadratic functions-vertical and horizontal shifts, and stretches and shrinks. Students match the symbolic form of the...
Curated OER
Families of Functions
In this Algebra II learning exercise, 11th graders shift the absolute value function horizontally and vertically, stretch and shrink, and reflect parent function. The two page learning exercise contains three problems. Answers are not...
West Contra Costa Unified School District
Conics Introduction and Parabolas
Where did conic sections get their name? The equation and graph of a parabola are developed from the definition of the conic section. Teacher examples on graphing the equation and writing an equation from the graph round out the plan.
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