Function Transformation (video lessons, examples and solutions)

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Graphs Of Functions
Parent Functions And Their Graphs
Transformations Of Graphs
More Pre-Calculus Lessons
Common Vi xử lý Core (Functions)

We shall learn how to lớn 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.

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Common Core: HSF-BF.B.3

The following table gives the transformation rules for functions: Vertical and horizontal translations, Reflection over the x-axis and y-axis, Vertical and horizontal stretch, Vertical and horizontal compression. Scroll down the page for examples and solutions on how to lớn use the transformation rules.

Transformation Rules Functions

Function Transformations: Horizontal And Vertical Stretches And Compressions

This video clip explains to lớn graph graph horizontal and vertical stretches and compressions in the form a*f(b(x-c))+d. This video clip 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.

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Function Transformations: Horizontal And Vertical Translations

This video clip explains to lớn graph graph horizontal and vertical translation in the sườn af(b(x-c))+d. This video clip 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

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Functions Transformations: A Summary

This video clip reviews function transformation including stretches, compressions, shifts left, shifts right, and reflections across the x and nó axes.

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Identify Function Translations Using Function Notation

This video clip explains how to lớn identify a shift up, down, left, and right given the translation in function notation.

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Graphing Multiple Function Transformations - Part 1 of 2

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Graphing Multiple Function Transformations - Part 2 of 2

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Try the miễn phí Mathway calculator and problem solver below to lớn practice various math topics. Try the given examples, or type in your own problem and kiểm tra your answer with the step-by-step explanations.