What is the difference between a vertical stretch and a vertical shrink?

The difference between a vertical stretch and a vertical shrink lies in how they affect the size of a graph or shape.

1. Vertical Stretch:
- A vertical stretch is a transformation that increases the vertical size of a graph or shape.
- It occurs when the vertical values of the graph or shape are multiplied by a factor greater than 1.
- This stretches the graph or shape vertically, making it taller, while maintaining the horizontal dimensions.
- For example, if we have a function y = f(x) and apply a vertical stretch with a factor of 2, the new function would be y = 2f(x), resulting in the graph being stretched vertically by a factor of 2.

2. Vertical Shrink:
- A vertical shrink is a transformation that decreases the vertical size of a graph or shape.
- It occurs when the vertical values of the graph or shape are multiplied by a factor between 0 and 1.
- This shrinks the graph or shape vertically, making it shorter, while maintaining the horizontal dimensions.
- For example, if we have a function y = f(x) and apply a vertical shrink with a factor of 0.5, the new function would be y = 0.5f(x), resulting in the graph being shrunk vertically by a factor of 0.5.

In summary, a vertical stretch increases the vertical size of a graph or shape, while a vertical shrink decreases the vertical size.

A vertical stretch and a vertical shrink are two transformations that can be applied to a function or graph.

A vertical stretch refers to increasing the vertical size or length of the graph. It stretches the graph vertically away from the x-axis. On the other hand, a vertical shrink refers to decreasing the vertical size or length of the graph. It shrinks the graph vertically towards the x-axis.

To understand the difference between a vertical stretch and a vertical shrink, you need to know about the scaling factor. The scaling factor is a number that determines how much the graph will be stretched or shrunk vertically.

For a vertical stretch, the scaling factor is greater than 1. To perform a vertical stretch, multiply the y-coordinates of each point on the graph by the scaling factor. This will stretch the graph vertically, making it taller and more spread out.

For example, if the scaling factor is 2, then every y-coordinate will be multiplied by 2. So, a point (x, y) on the original graph will become (x, 2y) on the stretched graph. This results in a graph that is twice as tall as the original.

On the other hand, for a vertical shrink, the scaling factor is between 0 and 1. To perform a vertical shrink, divide the y-coordinates of each point on the graph by the scaling factor. This will shrink the graph vertically, making it shorter and compressed.

For example, if the scaling factor is 0.5, then every y-coordinate will be divided by 0.5. So, a point (x, y) on the original graph will become (x, y/0.5) on the shrunk graph. This results in a graph that is half as tall as the original.

In summary, the difference between a vertical stretch and a vertical shrink lies in the scaling factor. A vertical stretch increases the vertical size of the graph, while a vertical shrink decreases the vertical size of the graph.

They're just two sides of the same operation. Stretch implies enlarging, shrink implies reducing.

So, if someone says to stretch y by a factor of 2, you'd naturally think of doubling the size of y.

Similarly, if they say to shrink y by a factor of 2, you'd divide by 2.