for F(x) = /x-2/ (absolute value)
When you graph this problem, does it have a straight line or a "v" line?
To determine the shape of the graph of the function f(x) = |x-2|, let's break it down into two cases:
1. When (x - 2) ≥ 0:
In this case, the absolute value |x-2| becomes (x-2), so the function simplifies to f(x) = x-2. This is the equation of a straight line with a slope of 1 passing through the point (2, 0).
2. When (x - 2) < 0:
In this case, the absolute value |x-2| becomes -(x-2), so the function simplifies to f(x) = -(x-2) = -x + 2. This is also the equation of a straight line with a slope of -1 passing through the point (2, 0).
Thus, both cases result in straight lines, and these lines meet at the point (2, 0). Since the function changes its behavior at x = 2, it creates a "V" shape where the absolute value function transitions from one straight line to the other.
In summary, the graph of f(x) = |x-2| consists of two straight lines that intersect at the point (2, 0), forming a "V" shape.