Algebra 2. Transformation of Fucntions.

In summary, vertical compression involves squishing points towards the x-axis while horizontal compression involves squishing points towards the y-axis. It is important to note that invariant points for each transformation are located on the respective axis. However, there are cases where a transformation can be equivalent to another relative to a different axis. An example is the function f(x) = 4x^2, which is a vertical stretch of y = x^2 by a factor of 2, but is also equivalent to a horizontal compression by a factor of 1/2.
  • #1
njkid
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0
Whats the difference between "Vertical Compression" and "Horizontal Compression"? Can you give me couple example? Thank you.
 
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  • #2
A vertical compression is "squishing" all points towards the x-axis, it is also important to rember that the invariant points in such a transformation are ON the x-axis. A horizontal compression is "squishing" all points towards the y-axis. It is important to remember that all invariant points are on the y-axis. However, there are some cases where a transformation is equivalent to another transformation relative to a different axis.
Consider the function [tex]f(x) = 4x^2 [/tex] This is a transformation of the graph of [tex]y = x^2[/tex] vertically stretched by a factor of 2. However, this is also equivalent to a horizontal compression by a factor of 1/2.
 
  • #3
Thank you very much.
 

Related to Algebra 2. Transformation of Fucntions.

1. What is a transformation of a function in Algebra 2?

A transformation of a function is a change in the position, shape, or orientation of the graph of a function. It can be achieved by applying specific mathematical operations to the original function.

2. What are the different types of transformations in Algebra 2?

There are four main types of transformations: translations, reflections, dilations, and rotations. Each of these transformations has a specific effect on the graph of a function.

3. How do I determine the type of transformation in a given function?

The type of transformation can be determined by looking at the equation of the function. Translations are indicated by adding or subtracting a constant value to the function, reflections are indicated by a negative coefficient, dilations are indicated by a coefficient other than 1, and rotations are indicated by trigonometric functions.

4. How do I graph a transformed function in Algebra 2?

To graph a transformed function, start by plotting the original function. Then, apply the specific transformation to each point on the original graph. For example, if the function is translated 3 units to the left, you would subtract 3 from the x-coordinate of each point on the original graph to get the new points for the transformed graph.

5. How do transformations affect the domain and range of a function?

Transformations do not affect the domain of a function, as it remains the same for both the original and transformed function. However, the range of a transformed function may change depending on the type of transformation. For example, a reflection or rotation may change the range, but a translation or dilation will not.

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