Vertical Translation
Vertical translation slides a function graph up or down along the -axis without changing its shape. Every point moves by the same vertical distance, as if the entire graph were lifted or lowered.
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Vertical translation slides a function graph up or down along the -axis without changing its shape. Every point moves by the same vertical distance, as if the entire graph were lifted or lowered.
If we have a function , then vertical translation produces a new function where is the translation constant.
For any function , vertical translation is defined as:
The direction of the shift follows these rules:
The linear function shows that a vertical translation leaves the slope unchanged.
The graph shows:
The same translation rule applies to the quadratic function .
The vertices make the displacement explicit:
Vertical translation preserves the original shape of the graph. The distance between points on the graph remains the same, only the vertical position changes.
If point is on the graph of , then after vertical translation by , that point becomes on the graph of .
If the range of the original function is , then the range after vertical translation becomes .
For the exponential function , the vertical translation also moves the horizontal asymptote.
For exponential functions:
Given the function . Determine the equation of the function resulting from vertical translation upward by .
If the graph of function is translated vertically downward by , determine:
Function undergoes vertical translation such that point becomes . Determine the translation constant value and the equation of the resulting translated function.
Vertical translation upward by :
Equation of the resulting translated function:
Point on becomes , meaning vertical translation by upward. Equation of the translation result:
Published: . Updated: .
Visualization: