Terri's project for the Math Fair was a magnificent black box that she called a function machine. If you put 3 into her machine, the output would be 8 . If you put in 10 , the output would be 29 ; and if you put in 20 , it would be 59 . Homework Help a. What would her machine do to the input 5 ? What about -1 ? What about \( x \) ? Making an input \( \rightarrow \) output table may help. b. Write an equation for Terri's machine.

Terri’s function machine seems to follow a pattern! Let’s analyze the input-output pairs: (3 → 8), (10 → 29), and (20 → 59). By examining these, we notice a consistent increase. It seems the machine is applying the equation \( f(x) = 3x - 1 \). For input 5, the machine would output \( f(5) = 3(5) - 1 = 14 \). For -1, the output would be \( f(-1) = 3(-1) - 1 = -4 \). To summarize the equation: Terri's magnificent function machine operates on the inputs with a formula that multiplies by 3 and subtracts 1. Get ready to wow the crowd with your table and equation at the fair! Inputs will produce outputs like magic, and everyone will want to know how you did it!