vertical translation up
In mathematics, a vertical translation refers to the shifting of a graph or function in the vertical direction
In mathematics, a vertical translation refers to the shifting of a graph or function in the vertical direction. It involves moving the graph or function up or down by a certain amount. A vertical translation is also known as a vertical shift or vertical displacement.
To perform a vertical translation, you need to determine the amount and direction of the shift. If the shift is positive, it means moving the graph or function upward, and if it is negative, it means moving it downward.
Let’s consider an example to illustrate the concept of vertical translation. Say we have the function f(x) = x^2. We want to perform a vertical translation upward by 3 units.
To shift the graph of f(x) upward by 3 units, we need to add 3 to the equation:
g(x) = f(x) + 3 = x^2 + 3
As a result, every y-coordinate of the graph of f(x) will increase by 3 units. The entire graph will be shifted vertically upward by the determined amount.
Alternatively, if we want to shift the graph downward by 2 units, we subtract 2 from the equation:
h(x) = f(x) – 2 = x^2 – 2
In this case, every y-coordinate of the graph of f(x) will decrease by 2 units, causing the whole graph to shift vertically downward.
It’s worth noting that the horizontal position of the graph or function remains unchanged during a vertical translation. Only the vertical positioning is affected.
In summary, a vertical translation involves shifting a graph or function upward or downward by a certain amount. By adding or subtracting the desired value to the equation, you can perform a vertical translation.
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