Understanding Vertical Shifting: A Guide to Moving Graphs Up or Down Along the Y-Axis in Math

Vertical shifting

Vertical shifting refers to the movement of a graph of a function up or down along the y-axis

Vertical shifting refers to the movement of a graph of a function up or down along the y-axis. It occurs when a constant value is added or subtracted to the function.

To understand vertical shifting, it is important to grasp the concept of the parent function, which is the most basic form of the function before any transformations are applied.

Let’s take the example of a linear function, f(x) = mx + b. The parent function of this linear equation is a straight line with a y-intercept of b and a slope of m.

Now, let’s consider the effect of adding or subtracting a constant value, h, to the function.

1. If h > 0: Adding a positive constant value h to the function f(x) results in shifting the graph vertically upwards. The whole graph moves up by h units.

For example, if f(x) = mx + b, then the transformed function would be f(x) + h = mx + (b + h).

2. If h < 0: Adding a negative constant value h to the function f(x) leads to shifting the graph vertically downwards. The entire graph moves down by h units. Continuing with the earlier example, if f(x) = mx + b, then the transformed function would be f(x) + h = mx + (b - |h|). It's important to note that the vertical shift does not affect the slope of the function, only the y-intercept. The slope remains the same. Vertical shifting is not limited to linear functions but can also be applied to other types of functions, including quadratic, exponential, or trigonometric functions. The same principles of adding or subtracting a constant value to the function apply to these functions as well. In summary, vertical shifting involves moving the graph of a function up or down along the y-axis by adding or subtracting a constant value to the function. It changes the y-intercept of the function without affecting the slope.

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