You can
put this solution on YOUR website!=\left\{\begin{array}{ll} 3x+5 & \ x < -2 \\ x+2 & \ x \ge -2 \end{array}\right.)
Remember, a piecewise function is simply a function composed of different functions. These functions are defined on "pieces" of the domain. So in the case of the given function
the two equations
and
are defined for
and
respectively. So what this means is that you graph the equation
ONLY if
. Otherwise, you graph
(since it is defined for
)
So the graph will look like this:
Graph of the given piecewise function where the red line is
(only drawn if
) the green line is
(only drawn if
)
Note: there is an open circle at (-2,-1) and a closed circle at (-2,0).
So because
, this means that we'll use
to find
Because the function
is defined for values
, this means that
Start with the second expression of the piecewise function
Plug in
Add
So
(