For AI agents: use /llms.txt for the Nakafa content index.
Vertical dilation is a geometric transformation that changes the size of a function graph vertically, like stretching or compressing a rubber band up and down. Imagine pulling a photo with both hands, one above and one below, then stretching or compressing it vertically without changing the width of the photo.
If we have a function , then vertical dilation produces a new function where is the scale factor that determines how much the vertical size changes.
For any function , vertical dilation is defined as:
Where is the scale factor that affects the transformation:
Let's see how vertical dilation works on the quadratic function with various scale factors.
From the visualization above, we can observe:
Now let's apply the same concept to the linear function .
Notice that:
If point is on the graph of , then the corresponding point on the graph of is .
If the range of the original function is , then the range after vertical dilation with factor becomes .
Let's look at vertical dilation on the exponential function .
For exponential functions:
Let's see what happens when the scale factor is negative.
When the scale factor is negative:
Given the function . Determine the equation of the function resulting from vertical dilation with scale factor .
If the graph of function undergoes vertical dilation with factor , determine:
Function undergoes vertical dilation with factor . Determine the vertex of the resulting dilated function.
Vertical dilation with factor :
Equation of the resulting dilated function:
The original function has its vertex at . After vertical dilation with factor : , the vertex becomes .
Visualization:
