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).
Showing a random 20 of 50 problems.
Example 1
easyThink of as a machine. Describe the sequence of operations applied to input , then evaluate and find the input that gives output .
Example 2
challengeMachines: and . Find an input with .
Example 3
mediumTwo machines: doubles, adds 3. Find .
Example 4
easyMust the inputs of a function be numbers?
Example 5
challengeGiven , find a function so that .
Example 6
mediumFor , find the input that gives output .
Example 7
easyIs the same as ?
Example 8
easyDoes mean multiplied by ?
Example 9
mediumIf , which input is NOT allowed, and why (input-output view)?
Example 10
easyFor , fill in the table: .
Example 11
mediumIf and , is a function? Is it one-to-one?
Example 12
easyA function maps each student to their birth year. Is birth year the input or the output?
Example 13
easyIn , which number is the input and which is the output?
Example 14
easyIf squares its input, what is ?
Example 15
mediumFor , find .
Example 16
mediumIf and , find .
Example 17
hardIf , find the inverse machine that recovers from .
Example 18
mediumIf and , , find and .
Example 19
mediumFor , find the input that produces output .
Example 20
easyCan two different inputs share the same output in a function?