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...

In this vertical and horizontal shift of functions, learners describe the period, amplitude, horizontal shift and vertical shift of each given function. This three-page worksheet contains seven multi-step problems.

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.

Young scholars explore the concept of sine and cosine.  In this sine and cosine instructional activity, students work in groups to graph sine and cosine functions.  Young scholars examine how coefficients in various parts of...

Students 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 function to...

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.

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...

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...

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.

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...

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.

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 lesson in a 26-part series focuses on horizontal...

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...

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.

Just like a painting or the symbols on a flag, quilts can express ideas that reflect a cultural context, space, and time. The class discusses the history of quilt making throughout US history and what different types of quilts mean. They...

Learners use sliders to change the parameters of functions and examine how shifting parameters affects a graph. They identify the parameters of functions, find vertical and horizontal stretches, then calculate the scale factor and other...

Discover the connection between vectors and translations. Through the instructional activity, learners see the strong relationship between vectors, matrices, and translations. Their inquiries begin in the two-dimensional plane and then...

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...

Students factor quadratic equations. In this algebra lesson, students apply the binomial square theorem to solve quadratics. They complete the square and use the complex number system to solve for the roots.

Looking for a complete go-to guide for the standard form of conics? This five-page packet does a nice job of connecting conics to prior knowledge of functions and transformations. Adapt the resource as Algebra II lesson plan...

Find relationships between the structure of a function and its graph. An engaging lesson explores seven parent functions and their graphs. Learners match functions to their graphs and describe transformations.

Learners create a timeline and scan pictures for it. In this timeline lesson, students use an interview of a family member to create a timeline for that person. They scan photographs to add to their computer made timeline. 

In this Algebra II worksheet, 11th graders shift the absolute value function horizontally and vertically, stretch and shrink, and reflect parent function. The two page worksheet contains three problems. Answers are not provided. 

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...