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HomeHomework HelpmathematicsTransformations of Functions

Transformations of Functions

Transformations of functions involve shifting, stretching, or reflecting the graph of a function to create new functions with different properties. These transformations are essential for understanding how changes in the function's equation affect its graphical representation.

intermediate
2 hours
Mathematics
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Overview

Transformations of functions are essential for understanding how to manipulate and analyze graphs. By learning about translations, reflections, stretching, and compressing, students can gain a deeper insight into the behavior of functions. These transformations allow for practical applications in va...

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Key Terms

Function
A relation that assigns exactly one output for each input.

Example: f(x) = x² is a function.

Translation
A shift of a graph in a specific direction.

Example: f(x) + 3 shifts the graph up by 3.

Reflection
Flipping a graph over a line, such as the x-axis or y-axis.

Example: -f(x) reflects the graph over the x-axis.

Stretching
Increasing the height of a graph, making it steeper.

Example: 2f(x) stretches the graph vertically.

Compression
Decreasing the height of a graph, making it less steep.

Example: 0.5f(x) compresses the graph vertically.

Horizontal Shift
Moving a graph left or right.

Example: f(x - 2) shifts the graph right by 2.

Related Topics

Quadratic Functions
Study the properties and transformations of quadratic functions.
intermediate
Exponential Functions
Explore transformations specific to exponential functions and their graphs.
intermediate
Absolute Value Functions
Learn about the transformations of absolute value functions and their unique shapes.
intermediate

Key Concepts

TranslationReflectionStretchingCompression