Mastering Horizontal Shifting in Mathematics: How to Displace Graphs along the X-Axis

Horizontal Shifting

In mathematics, horizontal shifting refers to the displacement of a graph horizontally along the x-axis

In mathematics, horizontal shifting refers to the displacement of a graph horizontally along the x-axis. This shifting can be described using algebraic notation.

To perform a horizontal shift, you can modify the equation of a function by adding or subtracting a value inside the parentheses. Let’s assume we have a function y = f(x), and we want to shift it horizontally by a value c units.

1. Shifting Right:
To shift the graph of y = f(x) c units to the right, we add c inside the parentheses. This can be represented as y = f(x – c).
For example, if we have the function y = x^2 and want to shift it 2 units to the right, we modify the equation to y = (x – 2)^2. This means that each x-coordinate in the original function is decreased by 2.

2. Shifting Left:
To shift the graph of y = f(x) c units to the left, we subtract c inside the parentheses. This can be represented as y = f(x + c).
For example, if we have the function y = x^2 and want to shift it 3 units to the left, we modify the equation to y = (x + 3)^2. This means that each x-coordinate in the original function is increased by 3.

It’s essential to note that positive values of c shift the graph to the right, while negative values shift it to the left. The magnitude of c represents the distance of the shift.

These horizontal shifts affect the position of the function’s graph, but they do not change the shape of the graph itself. The shape remains the same, but it moves along the x-axis.

Remember to always indicate the direction (left or right) and the magnitude (how far) of the shift when describing horizontal shifting.

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