Understanding Horizontal Shift in Mathematics | Exploring the Notation Y = f(x+c)

Y=f(x+c)

In mathematics, the notation “Y = f(x+c)” represents a function where the input variable is shifted horizontally by a constant amount c

In mathematics, the notation “Y = f(x+c)” represents a function where the input variable is shifted horizontally by a constant amount c. Here’s a more detailed explanation:

– The letter “Y” represents the output or dependent variable. It signifies the value of the function corresponding to a given input.
– “f()” indicates the function being used. This notation can represent any mathematical function.
– “x” represents the input or independent variable. It is the value for which we want to determine the corresponding output value.
– “+c” is the constant term that is added to the input variable. It shifts the graph of the function horizontally by c units to the left if c is negative (c < 0) or to the right if c is positive (c > 0). If c is zero (c = 0), then the graph is not shifted.

To understand this concept better, let’s consider an example. Let’s say we have the following function:

Y = f(x+2)

If we have a specific value for x, let’s say x = 3, then we can substitute it into the function to determine the corresponding value for Y. However, before substituting, we need to consider the shift of the input variable.

For x = 3, the term x+2 becomes 3+2 = 5. Therefore, the function can be rewritten as:

Y = f(5)

Now, we can substitute the value 5 into the function f() to find the value of Y. The specific value of Y depends on the function f() itself.

Overall, the equation Y = f(x+c) represents a function where the input variable x is shifted horizontally by c units.

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