Understanding the Transformation of Functions: Y = f(x + c) – Explained

Y=f(x+. c)

The equation Y = f(x + c) represents a transformation of the function f(x) by a translation of magnitude c to the left (if c is positive) or to the right (if c is negative)

The equation Y = f(x + c) represents a transformation of the function f(x) by a translation of magnitude c to the left (if c is positive) or to the right (if c is negative). Let’s explore this transformation in more detail:

1. Translation: A translation is a geometric transformation that shifts the graph of a function horizontally or vertically without altering its shape. In our case, the translation is horizontal, specifically by c units.

2. x + c: The input variable x is added to c in the equation. If x = 0, then f(x + c) becomes f(c). This means that the value c acts as a shift in the x-axis. Suppose c = 2, then the point (2, f(c)) on the original graph of f(x) will be shifted to (0, f(2)) on the transformed graph.

3. The graph: The transformed graph of Y = f(x + c) will be obtained by taking each point (x, f(x)) on the graph of the original function f(x) and shifting it horizontally c units. If c is positive, this means shifting the graph to the left, and if c is negative, it means shifting the graph to the right.

To graphically understand the transformation:
– For positive c: Each point on the original graph moves c units to the left. For example, if the original graph had a point (1, 3), it would move to (-c, 3).
– For negative c: Each point on the original graph moves c units to the right. For example, if the original graph had a point (-2, 5), it would move to (2-c, 5).

It’s important to note that the transformation Y = f(x + c) preserves the shape of the original graph but simply shifts it horizontally. The vertical shape and any other characteristics of the graph remain unchanged.

I hope this explanation helps you understand the concept of Y = f(x + c) and how it relates to the transformation of a function. If you have any further questions or need clarification, feel free to ask!

More Answers: