How to Scale a Function Vertically?
Scaling is a process of changing the size and shape of the graph of the function. In this blog post, you will learn how to vertical scaling.
![How to Scale a Function Vertically?](https://www.effortlessmath.com/wp-content/uploads/2022/03/Blog-How-to-Scale-a-Function-Vertically-512x240.jpg)
Vertical scaling refers to the shrinking or stretching of the curve along the \(y\)-axis by some specific units.
Related Topics
A step-by-step guide to vertical scaling
There are four types of transformation possible for a graph of a function, which are:
- Rotations
- Translations
- Reflections
- Scaling
In addition, scaling can be divided into two different types, e.g.
- Horizontal scaling
- Vertical scaling
Vertical scaling refers to changing the shape and size of a function graph along the \(y\)-axis and is done by multiplying the function by a fixed value.
The shape of the curve depends on the value of \(C\):
- If \(C > 1\), the graph stretches and makes the graph steeper.
- If \(C < 1\), the graph shrinks and makes the graph flatter.
How to do vertical scaling?
Let’s understand this with an example:
Suppose we have a basic quadratic equation \(f(x)=x^2\) and a graphical representation of the diagram is shown below.
![](https://www.effortlessmath.com/wp-content/uploads/2022/03/Untitledl.png)
If we want to vertically scale this chart, we have to follow the given steps:
Step 1: Select the constant with which we want to scale the function.
Here we have selected \(+2\).
Step 2: Write the new function as \(g(x)=C f(x)\), where \(C\) is the constant.
Here, the new function will be: \(g(x)=2 f(x)= 2 x^2\)
Step 3: Trace the new function graph by replacing each value of \(y\) with \(Cy\).
Here we need to replace the value of the \(y\)-coordinate by \(2y\).
The \(Y\) coordinates of each point in the graph are multiplied by \(±C\), and the curve shrinks or stretches accordingly.
Here we have the graph \(x\) and it is stretched in the \(y\)-direction with a factor of \(+2\).
![](https://www.effortlessmath.com/wp-content/uploads/2022/03/Untitledo.png)
Note: As we have scaled it with a factor of \(+2\) units, it has made the graph steeper.
Vertical Scaling – Example 1:
Vertically stretch the function \(y=(x+2)\) by a factor of two.
![](https://www.effortlessmath.com/wp-content/uploads/2022/03/Untitled85.png)
Exercises for Vertical Scaling
- Vertically stretch the function \(f(x)=x^3\) by a factor of \(-\frac{1}{3}\).
![This image has an empty alt attribute; its file name is Graphing-Rational-Expressions-Example-3-1.png](https://www.effortlessmath.com/wp-content/uploads/2021/12/Graphing-Rational-Expressions-Example-3-1.png)
![This image has an empty alt attribute; its file name is Graphing-Rational-Expressions-Example-3-1.png](https://www.effortlessmath.com/wp-content/uploads/2021/12/Graphing-Rational-Expressions-Example-3-1.png)
![This image has an empty alt attribute; its file name is answers.png](https://www.effortlessmath.com/wp-content/uploads/2019/12/answers.png)
![](https://www.effortlessmath.com/wp-content/uploads/2022/03/Untitledpp-1.png)
![](https://www.effortlessmath.com/wp-content/uploads/2022/03/Untitled11.png)
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