How to Transform Linear Functions

Transforming linear functions refers to the process of changing the shape or position of a linear function, while still preserving its linearity. This can be done by applying certain operations, such as translation, reflection, dilation, and rotation, to the function.

How to Transform Linear Functions

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Step-by-step to Transform Linear Functions

Here are some examples of how to transform linear functions:

  1. Translation: To translate a linear function up or down, you can add or subtract a constant from the \(y\)-coordinate. For example, \(y = 2x + 1\) can be translated up \(2\) units by adding \(2\) to the \(y\)-coordinate, resulting in \(y = 2x + 3\).
  2. Reflection: To reflect a linear function across the \(x\)-axis, you can negate the \(y\)-coordinate. For example, \(y = 2x + 1\) can be reflected across the \(x\)-axis by negating the \(y\)-coordinate, resulting in \(y = -2x – 1\).
  3. Dilation: To dilate a linear function, you can multiply the \(x\)-coordinate by a constant factor. For example, \(y = 2x + 1\) can be dilated by a factor of \(2\) by multiplying the \(x\)-coordinate by \(2\), resulting in \(y = 4x + 1\).
  4. Rotation: To rotate a linear function, you can change the slope of the function. For example, \(y = 2x + 1\) can be rotated \(90\) degrees by making the slope \(-\frac{1}{2}\), resulting in \(y = -\frac{1}{2}x + 1\)

Note: It’s important to notice that transformations does not change the type of function, it only changes the shape and position of the function.

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