Mastering Horizontal Translations: Shifting Graphs and Shapes to the Right

horizontal translation right

Horizontal translation to the right refers to shifting a graph or shape horizontally in the positive x-direction

Horizontal translation to the right refers to shifting a graph or shape horizontally in the positive x-direction.

To perform a horizontal translation right, you will need to add a positive value to the x-coordinates of the points on the graph or shape.

Let’s consider a simple example to illustrate this concept. Suppose we have the function f(x) = x^2, which represents a parabola centered at the origin.

To perform a horizontal translation right, let’s shift the graph 2 units to the right.

1. To find the new x-coordinate, add 2 to each x-coordinate of the original graph: x_new = x_old + 2.
For example, let’s say we have the point (1,1) on the original graph. After the translation, the new x-coordinate will be 1 + 2 = 3. The new point will be (3,1).

2. Repeat this operation for all the points on the graph.

By applying this translation, you will shift the entire graph of f(x) = x^2 two units to the right. The new graph will be represented by f(x) = (x – 2)^2.

It’s important to note that the sign convention for horizontal translations is opposite to the direction of the shift. In this case, we wanted to perform a translation to the right, so we added a positive value to the x-coordinates. If you wanted to shift the graph to the left, you would subtract a positive value from the x-coordinates.

Remember, this concept can also be applied to other shapes, such as polygons or circles. The key is to adjust the x-coordinates of each point accordingly to achieve the desired horizontal translation.

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