# Function Transformation

Videos and lessons to help High School students learn how to 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); 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.

Common Core: HSF-BF.B.3

Function Transformations: Horizontal and Vertical Stretches and Compressions
This video explains to graph graph horizontal and vertical stretches and compressions in the form a*f(b(x-c))+d. This video looks at how a and b affect the graph of f(x).

af(x): a > 1, stretch f(x) vertically by a factor of a
af(x): 0 < a < 1, compress f(x) vertically by a factor of a
f(bx); b > 1, compress f(x) horizontally
f(bx); 0 < b < 1, stretch f(x) horizontally.

Function Transformations: Horizontal and Vertical Translations
This video explains to graph graph horizontal and vertical translation in the form a*f(b(x-c))+d. This video looks at how c and d affect the graph of f(x).

f(x + c): shift f(x) c units left
f(x − c): shift f(x) c units right
f(x) + d: shift f(x) d units up
f(x) − d: shift f(x) d units down

Functions Transformations: A Summary
This video reviews function transformation including stretches, compressions, shifts left, shifts right, and reflections across the x and y axes.

F.BF.3 - Identify the Effect of Translations on functions.

Ex: Identify Function Translations using Function Notation
This video explains how to identify a shift up, down, left, and right given the translation in function notation.

Graphing Multiple Function Transformations - Part 1 of 2.

Graphing Multiple Function Transformations - Part 2 of 2.

Wolfram Function Transformations
This Demonstration allows you to investigate the transformation of the graph of a function f(x) to af(b(x - c)) + d for various values of the parameters a, b, c, and d. In addition to showing the original and transformed curves, it displays an individual movable point on the original curve and the image of the point on the transformed curve. The Demonstration also divides the original curve into two portions and shows the images of these two portions on the transformed curve to emphasize how negative values can affect the transformation.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.