Vertical compression is a transformation that makes a graph shorter or taller by changing its y-values. In Intermediate Algebra, you see it when graphing functions like logarithms and comparing how different scale factors affect the shape.
Vertical compression is a graph transformation in Intermediate Algebra that changes the y-values of a function without changing its x-values. If you multiply the whole function by a number between 0 and 1, the graph gets squeezed toward the x-axis. If the multiplier is greater than 1, the graph stretches vertically instead of compressing.
The basic rule looks like f(x) = a \cdot g(x), where a is the vertical scale factor. Every output value gets multiplied by a, so the graph keeps the same x-intercepts, domain, and left-to-right shape, but the heights change. That is why a graph can look flatter or steeper even though the horizontal input values are unchanged.
A good way to picture it is with a parent function. If y = log(x) and you change it to y = \frac{1}{2}log(x), every point on the graph drops to half its original height. A point like (10, 1) on the parent graph would move to about (10, 0.5). The x-value stays put, but the y-value shrinks.
This is where the word compression can be a little confusing. In many classes, students hear compression and think only of the graph getting smaller. That is true for factors between 0 and 1. But when the scale factor is bigger than 1, the graph is actually vertically stretched. So the transformation rule is the same, but the effect depends on the multiplier.
For logarithmic functions, vertical compression often shows up when comparing graphs with different bases or with a coefficient in front of the log. A larger base can make the graph look more compressed vertically, while a smaller coefficient like 1/3 makes the graph less steep. The main idea is that the y-values change by a consistent factor, not by a fixed amount.
Vertical compression shows up any time you graph logarithmic functions, compare transformed functions, or describe how a coefficient changes a parent graph in Intermediate Algebra. If you can spot the vertical scale factor, you can predict the new graph much faster than plotting every point from scratch.
It also helps you read function behavior correctly. Two graphs can have the same domain and the same x-intercepts, but one may have much smaller outputs because its y-values were compressed. That matters when you are asked to match equations to graphs, describe transformations in words, or explain why one log graph looks flatter than another.
This term is especially useful with logarithms because the vertical scale changes the height of the curve around the same x-values. In real-world modeling, that can change how quickly values appear to grow or flatten on a graph, such as when comparing scales like decibels or earthquake magnitude. The graph may still represent the same pattern, but the visual spacing changes how you interpret the outputs.
If you know how vertical compression works, you can also avoid a common error: mixing it up with horizontal changes. Vertical compression multiplies outputs, not inputs. That distinction shows up again and again in graphing problems, transformation questions, and mixed function review.
Keep studying Intermediate Algebra Unit 10
Visual cheatsheet
view galleryAmplitude
Amplitude is the height measure students often associate with waves and periodic graphs. Vertical compression lowers that height when the graph is multiplied by a factor between 0 and 1. In sine or cosine graphs, a smaller vertical scale factor makes peaks and troughs closer to the center line, which is why amplitude changes are easy to spot on a transformed graph.
Stretch
Stretch is the opposite direction from compression when the multiplier is greater than 1. Instead of pulling the graph toward the x-axis, it pushes y-values farther away. In Intermediate Algebra, noticing whether a factor causes a stretch or compression helps you read function transformations before you start plotting points.
Shrink
Shrink is the everyday word for what happens when a graph is vertically compressed. The outputs get smaller by the same factor, but the x-values stay the same. This makes it easier to compare a transformed graph with its parent function, especially when you are checking a logarithmic graph against the original curve.
Parent Function
The parent function is the original graph before any transformations are applied. Vertical compression is easiest to see when you compare the transformed graph to its parent, because the shape stays recognizable while the y-values change. For logarithmic functions, the parent graph gives you the baseline curve that the coefficient then compresses or stretches.
A graphing problem may give you a logarithmic equation and ask how the graph changed from its parent function. You would look at the coefficient in front of the log, decide whether the graph is vertically compressed or stretched, and then describe how the y-values changed. If the coefficient is between 0 and 1, the graph is compressed toward the x-axis.
You may also be asked to match an equation to a graph. In that case, compare the steepness and height of the curve to the parent logarithm, then check whether the x-values stayed in the same places. A common mistake is calling a change in steepness a horizontal shift, but vertical compression only affects the outputs. On quizzes and problem sets, you usually show this by writing the transformation rule, sketching the graph, or explaining the effect on key points.
Vertical compression and vertical stretch both change the y-values of a graph, but they work in opposite ways. A compression uses a multiplier between 0 and 1, which pulls the graph toward the x-axis. A stretch uses a multiplier greater than 1, which pushes the graph farther away from the x-axis.
Vertical compression changes the y-values of a graph while leaving the x-values in place.
A multiplier between 0 and 1 causes compression, which makes the graph look shorter or flatter.
A multiplier greater than 1 causes a vertical stretch, not a compression.
In Intermediate Algebra, vertical compression shows up often in logarithmic graphs and function transformations.
The easiest way to track it is to compare a transformed graph to its parent function and watch how the heights change.
Vertical compression is a transformation that multiplies all the y-values of a function by a factor between 0 and 1. The graph keeps the same x-values, but it gets squeezed toward the x-axis. In Intermediate Algebra, you usually see this when graphing transformed logarithmic functions.
Check the coefficient in front of the function. If it is a fraction between 0 and 1, the graph is vertically compressed. The shape stays the same, but every point moves closer to the x-axis because the y-values are smaller.
No. They are related, but opposite. Vertical compression uses a factor between 0 and 1, while vertical stretch uses a factor greater than 1. Both change output values, but one shrinks the graph and the other makes it taller.
It changes how tall the logarithmic curve looks without changing where the inputs are. A coefficient like 1/2 in front of a log function makes the graph less steep and compresses its y-values. This is a common transformation when comparing logarithmic graphs with different scale factors.