The graph of a piecewise defined function is given Find a fo

The graph of a piecewise defined function is given. Find a formula for the function in the indicated form.

Solution

In the graph the desired equation is

(1) In the given line graph
x <= -1
eqn of line
(y+6) = m(x-4)
m = (y2-y1)/(x2-x1)
m = (4-4)/(-6+1)
m = 0
so
(y+6) = 0
y = -6
on x axis fro -1 to -8
the list no is -8

(2) -1 <= x <= 2
eqn of line
(y-2) = m(x-2)
m = (y2-y1)/(x2-x1)
m = (2-5)/(2+1)
m = -3/3
m = -1

(y-2) = -1(x-2)
y = -x+4
lies on negative x axis -1 to +2

(3) x > 2
eqn of line
(y-2) = m(x-6)
m = (y2-y1)/(x2-x1)
m = (6-2)/(2-1)
m = 4
(y-2) = 4(x-6)
y = 4x-22

lies on x axis from +2 to +6
Answer