horizontal translation
In mathematics, a horizontal translation refers to the shifting of a graph or object left or right along the x-axis without changing its shape
In mathematics, a horizontal translation refers to the shifting of a graph or object left or right along the x-axis without changing its shape.
To perform a horizontal translation, you need to add or subtract a constant value to the x-coordinate of each point on the graph or object. This constant value determines the direction and distance of the translation.
If you want to shift the graph or object to the right, you will add a constant value to each x-coordinate. For example, let’s say you have a graph defined by the equation y = f(x). To translate it horizontally to the right by a distance of ‘d’ units, you would use the equation y = f(x – d). By subtracting ‘d’ from each x-coordinate, you shift the graph ‘d’ units to the right.
Conversely, to shift the graph or object to the left, you will subtract a constant value from each x-coordinate. Using the same graph defined by y = f(x), to translate it horizontally to the left by a distance of ‘d’ units, you would use the equation y = f(x + d). By adding ‘d’ to each x-coordinate, you shift the graph ‘d’ units to the left.
It’s important to note that horizontal translations preserve the vertical position of the graph or object. The y-coordinate remains the same, only the x-coordinate is modified.
For example, consider the function f(x) = x^2. If we want to horizontally translate this graph 3 units to the right, we would rewrite the equation as f(x) = (x – 3)^2. This will shift the graph to the right, while maintaining the shape and vertical position of the original graph.
Similarly, if we want to translate the function f(x) = x^2 horizontally 2 units to the left, we would rewrite the equation as f(x) = (x + 2)^2. This will shift the graph to the left, while again preserving its shape and vertical position.
Remember, when performing horizontal translations, the sign of the constant value determines the direction of the shift. Positive values shift to the right, and negative values shift to the left.
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Understanding Vertical Translation in Mathematics: How to Shift a Graph or Function Up or Down Along the Y-axis