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.

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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