A vertical compression is a transformation that vertically stretches or shrinks a function. The domain and range of the function remain unchanged, but the y-coordinate of each point on the graph is multiplied by a constant. Vertical compressions can be represented as y = kf(x), where k is the constant multiplier. For example, if k > 1, the function will be stretched vertically; if k < 1, the function will be shrunk vertically. Vertical compressions are commonly used to alter the amplitude of a function without affecting its other properties.
What is vertical compression?
Vertical compression is a type of data compression that reduces the height of an image while maintaining its width. This can be useful for reducing the file size of an image without sacrificing too much detail. Vertical compression is often used for images that are displayed on the web, where file size is a concern.
How does vertical compression work?
Vertical compression works by removing unnecessary pixels from the image. This is done by dividing the image into small blocks and then removing the pixels that are similar to the pixels in the surrounding blocks. The resulting image is smaller in height, but it retains the same level of detail as the original image.
Benefits of vertical compression
There are several benefits to using vertical compression:
- Reduced file size: Vertical compression can reduce the file size of an image by up to 50%. This can make it easier to store and share the image.
- Maintained quality: Vertical compression does not sacrifice too much detail, so the resulting image will still look good.
- Improved loading time: A smaller file size means that the image will load faster on the web.
Limitations of vertical compression
There are also some limitations to using vertical compression:
- Reduced resolution: Vertical compression can reduce the resolution of the image. This can make it less suitable for printing or other applications where high resolution is required.
- Artifacts: Vertical compression can sometimes introduce artifacts into the image. These artifacts can appear as lines or blocks of color.
Example of vertical compression
The following table shows an example of vertical compression. The original image is on the left, and the compressed image is on the right.
| Original image | Compressed image |
|---|---|
Question 1:
- What is meant by “vertical compression” in mathematics?
Answer:
- Vertical compression is a transformation that alters the height of a function’s graph, making it narrower or wider.
Question 2:
- How does vertical compression affect the y-values of a function?
Answer:
- Vertical compression reduces the absolute value of the function’s y-values, magnifying the distance between them and the x-axis.
Question 3:
- What is the form of the equation for a function that has undergone vertical compression?
Answer:
- The equation for a vertically compressed function is y = a * f(x), where “a” is a positive constant representing the magnitude of the compression.
Well, there you have it! Now you’re a vertical compression expert. Go on, impress your friends and family with your newfound knowledge. And if you’re feeling particularly adventurous, experiment with different vertical compressions on your own photos. Just remember to have fun and don’t be afraid to make mistakes. After all, that’s how we learn! Thanks for reading, folks! Be sure to visit again later for more photo editing tips and tricks.