Please review the concept of a function as an “Input-Output Machine” on page 205 of Section 2.3 on Functions.
Then, respond to at least one of the topics below for your initial post.
Describe a “real world” example of a function using this concept. Specify the domain (inputs), range (outputs), and the rule for the function that sends an input to a single output.
Describe a “real world” example of a relation (a set of ordered pairs) which is NOT a function. Explain why it is NOT an Input-Output Machine by giving an example of an input that gets sent to two different outputs.
A function is defined as a set of ordered pairs in which no first coordinate is repeated.
If you graph this set of ordered pairs in the xy-plane, which axis represents the domain (inputs) and which axis represents the range (outputs)? Explain.
Explain how a set of ordered pairs in the xy-plane which passes the Vertical Line Test is a function by using the concept of an Input-Output Machine.
For any real number x ≥ 0, let R(x) = any real number whose square is x.
Is R a function whose domain is all non-negative real numbers and whose range is all real numbers?
If R is a function, explain why.
If R is not a function, explain why, and explain how you could modify the range to make it a function.
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