Vertical & Horizontal Translations Quick Check
A vertical translation refers to the shifting of a function either up or down on the coordinate axis. This is done by adding or subtracting a constant value to the function.
Example: y = x² + 3 represents a vertical translation of the graph of y = x² three units upward.
A horizontal translation refers to the shifting of a function either to the left or to the right on the coordinate axis. This is done by adding or subtracting a constant value to the independent variable in the function.
Example: y = (x-2)² represents a horizontal translation of the graph of y = x² two units to the right.
To determine the direction and amount of the translation, look at the added or subtracted value in the function. If it is added, the translation is in the opposite direction (up or left), and if it is subtracted, the translation is in the same direction (down or right).
To determine vertical and horizontal translations, you need to analyze the equation of a function. By examining the equation, you can identify the shifts in the graph from the original position.
Vertical Translation:
1. Look for the term that involves the variable y in the equation. This term determines the vertical shift. If there is no term involving y, the function has no vertical shift.
- If the term involving y is positive, the graph will shift upward.
- If the term involving y is negative, the graph will shift downward.
Horizontal Translation:
1. Look for the term that involves the variable x in the equation. This term determines the horizontal shift. If there is no term involving x, the function has no horizontal shift.
- If the term involving x is positive, the graph will shift to the right.
- If the term involving x is negative, the graph will shift to the left.
By considering these steps, you can identify the vertical and horizontal translations in a given equation.