Understanding Vertical Shifts in Math: Exploring the Function Y = f(x-c) for Shifting Graphs Right

Y=f(x-. c)

The function Y = f(x-c) represents a vertical shift of the function f(x) by c units to the right

The function Y = f(x-c) represents a vertical shift of the function f(x) by c units to the right. In other words, if you have a function f(x) and you want to move it c units to the right, you would use the function f(x-c).

To understand this concept visually, think of a graph. When you have the function f(x), it represents the original position of the graph. The variable x represents the horizontal axis, and f(x) represents the corresponding y-values on the vertical axis.

Now, if you want to shift this graph c units to the right, you would subtract c from the x-values. This means that the value of x-c is now the new x-value for the graph. Therefore, the function f(x-c) represents the new position of the graph, shifted c units to the right.

For example, let’s say you have the function f(x) = x^2, which is a simple quadratic function. If you want to shift this graph 3 units to the right, you would use the function f(x-3). The new function would be Y = f(x-3) = (x-3)^2.

To understand how this affects the graph visually, you can compare the original function f(x) = x^2 with the shifted function Y = f(x-3) = (x-3)^2. When you graph both functions, you will notice that the graph of Y = f(x-3) is identical to the graph of f(x), but it is shifted 3 units to the right.

In summary, the function Y = f(x-c) represents a vertical shift of the function f(x) by c units to the right. This means that the graph of Y = f(x-c) will have the same shape as the graph of f(x), but it will be shifted c units to the right.

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