Terri’s project for the Math Fair is a magnificent black box that she called a function machine. If you put $3$ into her machine, the output is $8$. If you put in $10$, the output is $29$; and if you put in $20$, the output is $59$.

1. What would her machine do to an input of $5$? What about $-1$? What about $x$? Making an input → output table may help.

   Hint (a):

   Look for a pattern.

   More Help (a):

   Try making a table and graphing the points.

   If the input is $x$, what is the output?

   Answer (a):

   $x$	$3$	$10$	$20$	$5$	$-1$
   $3x-1$	$8$	$29$	$59$	$14$	$-4$

2. Write an equation for Terri's machine.

   Answer (b):

   $f(x)=3x−1$