f(x)=2−x

The function you've provided is a linear function expressed as \( f(x) = 2 - x \). Here's a brief overview of its properties:

1. Slope & Intercept:

   • The slope of the function (the coefficient of \( x \)) is \( -1 \). This indicates that the function decreases as \( x \) increases.
   • The y-intercept (the value of \( f(x) \) when \( x = 0 \)) is \( 2 \). This means the graph of the function crosses the y-axis at the point \( (0, 2) \).

2. Graph:

   • The graph is a straight line that goes downwards from the left to the right, crossing the y-axis at \( (0, 2) \).
   • The x-intercept can be found by setting \( f(x) = 0 \): \[ 0 = 2 - x \implies x = 2 \] So the x-intercept is \( (2, 0) \).

3. Domain and Range:

   • The domain of the function (all possible inputs) is all real numbers, \( \mathbb{R} \).
   • The range (all possible outputs) is also all real numbers, \( \mathbb{R} \).

4. Behavior:

   • As \( x \) approaches infinity, \( f(x) \) approaches negative infinity.
   • As \( x \) approaches negative infinity, \( f(x) \) approaches positive infinity.

If you have any specific queries or require additional details (like finding the derivative, integral, or anything else related to this function), feel free to ask!