Translations
Key points
- Vertical translations are when a graph moves up or down.
- Added as a constant at the end of the equation.
- Horizontal translations are when a graph moves left or right.
- Expressed within the variable expression, with the sign switched.
Translations are when all of the points of a graph are all moved by the same amount, which “shifts” the line either vertically or horizontally.
Vertical translations of graphs occur when the whole graph is shifted either up or down.
- In equations, vertical translations are expressed as a constant added/subtracted at the end of the equation.
- A positive constant means the graph is moving up.
- Subtracting a constant means the graph is being shifted down.
Horizontal translations of graphs occur when the whole graph is shifted either left or right.
- In equations, horizontal translations are expressed as a constant added/subtracted within the variable expression.
- When a constant is being subtracted, the graph is being shifted to the right: f(x-h)
- When a constant is being added, the graph is shifting left: f(x+h)
- Values to the left are always negative, and values to the right are always positive, but not in the case of expressing horizontal translations in an equation.
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