How do you graph f(x)= -1/4|x-2|+2?

1 Answer

Socratic graph is inserted. See the explanation.

Explanation:

As 8 - 4y = abs(x-2) >= 0, y <=2.

Let me introduce the inverse operator abs(...)^(-1) for abs =

abs(...).

If g(y) = abs(f(x)), then

f(x) =

(abs)^(-1)(g(y)) = g(y), for f(x) >= 0 and

                          = - g(y), for #f(x) <= 0#.

Here, f(x) = x - 2 and g(y) = 8 - 4y. And so,

x -2 = 8 - 4y or x = 10 - 4y, for x-2 >= 0

x - 2= 4y - 8 or x = 4y - 6, for x - 2 <= 0.

The given equation is the combined equation, for these separate

piecewise equations

See the graph.

The vertex (2, 2) is the zenith of this pair.

graph{y+1/4|x-2|-2=0 [-20, 20, -10, 10]}