What Does a Vertical Stretch Mean?

Introduction

In mathematics, a vertical stretch is a transformation that changes the shape of a graph by making it taller or narrower. This transformation is applied to the y-values of the original graph, and it does not affect the x-values.

Concepts and Definitions

**Vertical Stretch Factor:** The vertical stretch factor, denoted by “a,” determines the amount by which the graph is stretched or compressed vertically.
**Stretching (a > 1):** When the vertical stretch factor is greater than 1, the graph is stretched vertically, making it taller and narrower.
**Compressing (0 < a < 1):** When the vertical stretch factor is between 0 and 1, the graph is compressed vertically, making it shorter and wider.

Equation of a Vertically Stretched Graph

The equation of a vertically stretched graph is obtained by multiplying the y-coordinate of the original graph by the vertical stretch factor “a.” For a graph represented by the equation y = f(x), the equation of the vertically stretched graph is:

y = a * f(x)

Examples

Stretching by a factor of 2: If the original graph has the equation y = x^2, the vertically stretched graph with a factor of 2 has the equation y = 2x^2.
Compressing by a factor of 0.5: If the original graph has the equation y = sin(x), the vertically compressed graph with a factor of 0.5 has the equation y = 0.5 * sin(x).

Step-by-Step Example

Let’s consider the graph of the function y = x^2. To vertically stretch this graph by a factor of 3, we follow these steps:

Multiply the y-coordinate by the stretch factor: y = 3x^2
Plot the points for the new graph by substituting different values of x into the new equation.

Conclusion

A vertical stretch is a transformation that modifies the height of a graph vertically. By understanding the concept and equation of a vertical stretch, you can effectively modify graphs and analyze their transformations.

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What Does A Vertical Stretch Mean