Understanding Horizontal Shifts in Functions | Exploring the Equation Y = f(x – c)

Y=f(x-c)

The equation Y = f(x – c) represents a transformation of a function f(x) by a horizontal shift to the right, or positive c units

The equation Y = f(x – c) represents a transformation of a function f(x) by a horizontal shift to the right, or positive c units. In other words, it is the same function f(x), but shifted horizontally to the right by the value of c.

Here’s how the transformation works:

1. Original function: Start with the original function f(x).
2. Horizontal shift: Take each x-value in the original function and subtract c from it. This shifts all points on the graph to the right by c units.
3. New function: The resulting function, given by Y = f(x – c), represents the graph of the original function shifted horizontally by c units to the right.

For example, let’s say we have the function f(x) = x^2, and we want to shift it to the right by 3 units. We can use the equation Y = f(x – 3) to represent the shifted function.

To find the coordinates of the points on the shifted graph, we can substitute the shifted x-values into the original function. For instance, to find the new y-coordinate of the point (2,4) from the original function, we substitute x – c = 2 – 3 = -1 into the original function: f(-1) = (-1)^2 = 1. So, the point on the shifted graph would be (-1, 1).

In summary, the equation Y = f(x – c) represents a horizontal shift of the original function f(x) to the right by c units.

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