Curated OER
Trigonometric Graphs: Vertical Shift and Stretching
In this trigonometric graph worksheet students describe the period, amplitude and vertical shift of given functions. They graph the trigonometric function. This four-page worksheet contains 16 multi-step problems.
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.
Curated OER
MT-A141 PreCalculus: Worksheet 6.4
In this precalculus worksheet, 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 problems. ...
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...
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.
Varsity Tutors
Varsity Tutors: Hotmath: Practice Problems: Graphs of Trigonometric Functions
Hotmath provides 20 practice problems on graphs of trigonometric functions. Each of the practice problems include a step-by-step guide for solving their graphs.
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.
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.
McGraw Hill
Glencoe: Online Study Tools: Quiz on Graphs of Trigonometric Functions
Students show comprehension of advanced mathematical concepts in Trigonometry. The online quiz assesses the scholars on the graphs of trigonometric functions.
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.
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...
Purple Math
Purplemath: Graphing Trigonometric Functions
This resource explains how to relate constants in trigonometric function to amplitudes, vertical shifts, periods, and horizontal or phase shifts with the help of many solved examples for various trigonometric functions.
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,...