Function Definition

The given function is defined as f(x) = (x-2) / 1 for all real values of x. Let's break down and analyze this function step by step.

Function Notation

The function is represented by f(x), where f represents the name of the function and (x) denotes the input variable.

Understanding the Formula

The formula f(x) = (x-2) / 1 represents the relationship between the input value x and the output value f(x). In this case, the output value is obtained by subtracting 2 from the input value and dividing the result by 1.

Simplifying the Formula

Simplifying the formula further, we have f(x) = x - 2. Since dividing by 1 does not change the value, we can disregard it and rewrite the function as f(x) = x - 2.

Interpretation of the Function

The function f(x) = x - 2 represents a linear equation. It describes a straight line on a graph, where the value of f(x) is determined by subtracting 2 from the input value x.

Graphical Representation

To visualize the function, we can plot it on a graph. The x-axis represents the input values, while the y-axis represents the output values. By choosing different values for x, we can determine the corresponding values of f(x) and plot them on the graph.

Effects of Changing x

- When x is positive, f(x) will be x - 2 units below the x-axis.
- When x is negative, f(x) will be x - 2 units above the x-axis.
- When x is zero, f(x) will be -2, indicating that the graph intersects the y-axis at -2.
- When x increases, the value of f(x) will also increase by the same amount.
- When x decreases, the value of f(x) will also decrease by the same amount.

Conclusion

In summary, the function f(x) = (x-2) / 1 represents a linear equation where the output value is obtained by subtracting 2 from the input value. The graph of this function is a straight line that intersects the y-axis at -2. By understanding the function and its graphical representation, we can analyze how changing the input value x affects the output value f(x).