Texas Instruments
Graphs of Rational Functions
Take your kids on a tour of graphing rational functions. Using this TI lesson, high schoolers identify the end behavior of their functions. They find the domain and range, describe end behavior, and look at asymptotes and restrictions of...
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.
Hofstra University
New Functions From Old: Scaled and Shifted
Includes rules, examples, and sample problems on 6 different types of translations; vertical and horizontal shift, stretch, and reflection. Uses six basic functions (x, x^2, x^3, 1/x, x^1/2, and abs(x)) throughout examples, which makes...
Texas Education Agency
Texas Gateway: Transformations of Exponential and Logarithmic Functions
Given an exponential or logarithmic function, the student will describe the effects of parameter changes.
Paul Dawkins
Paul's Online Notes: Algebra: Transformations
Detailed math tutorial features notes and examples that take a look at vertical and horizontal shifts of graphs as well as reflections of graphs about the x and y-axis, often called transformations.
Ministry of Education and Universities of the Region of Murcia (Spain)
Ministerio De Educacion Y Ciencia: Transformaciones De Funcioness
In Spanish. In this interactive activity you will see a visual explanation of the different kinds of translations and dilation of functions.
California State University
Ca State University, San Bernadino: Graphing Techniques
A survey of math graphing techniques includes horizontal and vertical shifts, stretching, lines of symmetry, even and odd functions, and absolute value functions.
McGraw Hill
Glencoe: Quiz on the Translations of Sine and Cosine Functions
The online assessment demonstrates knowledge of advanced mathematical concepts in Pre-Calculus. The questions evaluate students on translations of sine and cosine functions. Topics include horizontal and vertical shifts.
Mangahigh
Mangahigh: Algebra: Translate Graphs Horizontally
Students learn about the concept of translating graphs by exploring a tutorial. They can then test their knowledge by taking a ten question assessment that increases in difficulty as they correctly answer questions.
Texas Instruments
Texas Instruments: Sine and Cosine
This set of questions measures knowledge of amplitude, horizontal and vertical shift, and periods of sine and cosine graphs. Questions are multiple-choice and true/false; solutions are included.
Khan Academy
Khan Academy: Modeling With Sinusoidal Functions: Phase Shift
Given the description of a real-world relationship, find the sinusoidal function that models it. The functions in this exercise have a phase (horizontal) shift. Students receive immediate feedback and have the opportunity to try...
Illustrative Mathematics
Illustrative Mathematics: F Bf, a Sse Building a General Quadratic Function
This task is a followup to the one called 'Building an explicit quadratic function.' In this one, learners follow the same process with a general quadratic function. The operations take place in the opposite order and the goal is to find...
Khan Academy
Khan Academy: Shift Functions
Shift functions horizontally and vertically, and practice the relationship between the graphical and the algebraic representations of those shifts. Students receive immediate feedback and have the opportunity to try questions repeatedly,...