f(x)=2-x

The function you've provided is \( f(x) = 2 - x \). This is a linear function, and we can analyze its various properties:

1. Slope and Y-intercept:

   • The function can be rewritten in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
   • For \( f(x) = 2 - x\):
     • Slope \( m = -1 \)
     • Y-intercept \( b = 2 \) (This means the graph crosses the y-axis at (0, 2)).

2. X-intercept:

   • To find the x-intercept, set \( f(x) = 0 \): \[ 0 = 2 - x \quad \Rightarrow \quad x = 2 \]
   • The x-intercept is at the point (2, 0).

3. Graph:

   • The graph of the function is a straight line that decreases from left to right (due to the negative slope). It crosses the y-axis at (0, 2) and the x-axis at (2, 0).

4. Domain and Range:

   • The domain of \( f(x) \) is all real numbers: \( (-\infty, \infty) \)
   • The range is also all real numbers: \( (-\infty, \infty) \)

5. Behavior:

   • As \( x \) increases, \( f(x) \) decreases. Specifically, for every increase of 1 in \( x \), \( f(x) \) decreases by 1.

If you need further information or a specific type of analysis about the function \( f(x) = 2 - x \), feel free to ask!