Horizontal Dilation

Basic Concepts of Horizontal Dilation

Horizontal dilation is a geometric transformation that changes the size of a function graph horizontally, like pulling or compressing a rubber band left and right. Imagine holding a photo with both hands on the left and right sides, then stretching or compressing it horizontally without changing the height of the photo.

If we have a function $f(x)$ , then horizontal dilation produces a new function $g(x) = f(kx)$ where is the scale factor that determines how much the horizontal size changes.

Function Transformations

Horizontal Dilation

Basic Concepts of Horizontal Dilation

Horizontal dilation is a geometric transformation that changes the size of a function graph horizontally, like pulling or compressing a rubber band left and right. Imagine holding a photo with both hands on the left and right sides, then stretching or compressing it horizontally without changing the height of the photo.

If we have a function $f(x)$ , then horizontal dilation produces a new function $g(x) = f(kx)$ where is the scale factor that determines how much the horizontal size changes.

Horizontal Dilation

Basic Concepts of Horizontal Dilation

Horizontal Dilation

Basic Concepts of Horizontal Dilation

Rules of Horizontal Dilation

Visualization of Horizontal Dilation

Horizontal Dilation on Linear Functions

Important Properties of Horizontal Dilation

Effect on Coordinate Points

Domain and Range

Axis Intercepts

Application Examples

Exponential Function

Horizontal Dilation with Negative Factor

Exercises

Answer Key