Question 152652
Let's sketch f(x) = -x + 1.  All linear equations can be represented as f(x) = mx + b. The m is the slope of the line. We know it has the same slope. Therefore, the graph above will have the same slope as f(x) = -x + 1. 
<br>The b is the y-intercept at the point (0,b). In this case, b = 1. So we know it intersects the y-axis at the point (0,1):
<br>{{{ graph( 200, 200, -5, 5, -5, 5, -x+1) }}}
<br>Now let's try to figure out what the reflection looks like. In order to be a reflection of f(x) = -x + 1, it should have the opposite slope and opposite y-intercept. 
<br>Since the slope of the original function is m = -1, the opposite slope would be  m = 1. 
<br>Since the intercept is one unit above the x-axis, the next time, it should be one unit below. That would be at the point (0,-1) or b = -1.
<br>Putting that all together:
r(x) = mx + b
r(x) = (1)x + (-1)
r(x) = x - 1
<br>Graphing that equation:
<br>{{{ graph( 200, 200, -5, 5, -5, 5, x-1) }}}
<br>Now let's graph both equations to make sure they are reflections of each other:
<br>{{{ graph( 200, 200, -5, 5, -5, 5, -x+1, x-1) }}}
<br>They are reflections of each other. Therefore, the answer is r(x) = x - 1.