Practice Input-Output View in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The input-output view of a function treats it as a black box: put in a value (input), get out a uniquely determined value (output), without worrying about the internal mechanism.

Like a vending machine: put in selection (input), get out snack (output).

Example 1

easy
Think of f(x) = 3x - 7 as a machine. Describe the sequence of operations applied to input x, then evaluate f(5) and find the input that gives output 14.

Example 2

medium
A function machine applies two operations in sequence: first square the input, then add 3. Write the function formula f(x), fill in a table for x \in \{-2,-1,0,1,2\}, and identify any symmetry.

Example 3

easy
A vending machine charges \1.50 per item. Write a function C(n) for the cost of n items, and find C(4) and the number of items for budget \9.

Example 4

medium
Two function machines are connected: machine A doubles the input, machine B subtracts 1. Find the combined output for input x=5, and write the combined formula.
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