Vertical Translation
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A vertical translation of a function refers to the process of shifting the function vertically up or down along the y-axis. This can be accomplished by adding or subtracting a constant value (k) to the output (y) of the function.
The general form of a vertical translation of a function f(x) is given by: y = f(x) + k where:
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For example, if the original function is f(x) = x^2, a vertical translation of 1 unit upward would be represented by:
y = x^2 + 1
The graph of the translated function will be shifted vertically by k units upward (or downward) compared to the graph of the original function.
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Consider the graph of y = f(x), then the graph of y=f(x)+ d is the vertical translation of the graph y=f(x). If ‘d’ is positive then the graph translations vertically upwards “d” units, if ‘d’ is negative then it moves vertically downwards “d” units. |
Interactive Graph
Use the interactive graph given below to visuvalize the vertical translation. Use the slider ‘d’ to change the values and observe the translation.
1. Vertical translation of Quadratic functions
Interactive Graph
Use the slider “d” to change the values in the interactive graph given below to see the vertical translation of the graph of y=x^2
2. Vertical translation of logarithmic functions
Interactive Graph
Use the slider “d” to change the values in the interactive graph given below to see the vertical translation of the graph of y=ln(x)
3. Vertical translation of exponential functions
Interactive Graph
Use the slider “d” to change the values in the interactive graph given below to see the vertical translation of the graph of y=exp(x)
3. Vertical translation of exponential functions
Interactive Graph
Use the slider “d” to change the values in the interactive graph given below to see the vertical translation of the graph of y=exp(x)