Understanding Rightward Shifting Functions | How Graphs Move to the Right as x Increases

a function is ____ if its graph moves ____ as x moves to the right

A function is called a “rightward shifting” function if its graph moves to the right as x moves to the right

A function is called a “rightward shifting” function if its graph moves to the right as x moves to the right.

When we say that a function is “rightward shifting,” it means that the graph of the function moves horizontally to the right as we increase the value of x.

To understand this concept better, let’s look at an example:

Consider the function f(x) = x^2. The graph of this function is a parabola that opens upward. If we plot this function on a graph, its vertex will be located at the origin (0,0). Now, if we have another function, g(x) = (x – 2)^2, the graph of this function will also be a parabola that opens upward. However, compared to f(x) = x^2, the graph of g(x) will be shifted two units to the right.

This means that as x increases, the corresponding y-values for g(x) will be the same as f(x), but the x-values will be shifted two units to the right. So, for example, when x = 1 for f(x), we get y = 1^2 = 1. But for g(x), when x = 1, we actually have x – 2 = 1 – 2 = -1, and substituting this into g(x) gives us y = (-1)^2 = 1. The corresponding y-values are the same, but the x-values are shifted to the right by two units.

In summary, a rightward shifting function is one whose graph moves horizontally to the right as x moves to the right.

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