To graph the function $f(x)$, we need to break it down into its piecewise components:

Function Definition:

• $f(x) = 3x + 14$ for $x < -5$
• $f(x) = x - 4$ for $x > 2$

Steps:

1. Graph for $x < -5$:
   The equation is $f(x) = 3x + 14$.

   • This is a straight line with slope 3 and y-intercept 14.
   • Since we are only interested in values where $x < -5$, we'll start from that point and move to the left.

2. Graph for $x > 2$:
   The equation is $f(x) = x - 4$.

   • This is a straight line with slope 1 and y-intercept -4.
   • We graph this only for values where $x > 2$.

There are no values defined for $-5 \leq x \leq 2$, so we leave that part of the graph blank.

Would you like me to provide more details on how these lines were obtained or visualize this graph?