Math CentralQuandaries & Queries


Question from Destanie:

What is the output if the input is -1???


It depends on the function. Suppose the function multiplies the input by 2 and then adds 5. If you input -1 to this function in multiplies -1 by 2 to get -2, and then it adds 5 to get -2 + 5 = 3. Mathematicians find this description of how the function works to be too cumbersome so they use algebraic notation to describe how the function works. Rather than say "the input to the function" every time we would say "let $x$ be the input to the function" and then the action of the function is

\[2 \times x + 5.\]

It is customary to also give functions names, so I am going to call this function $f.$ The description of what the function does to an input of $x$ is $2 \times x + 5$ and this is written

\[f(x) = 2x + 5.\]

Your textbook might then say "For the function $f(x) = 2x + 5$ what is the output if the input is -1?" the answer is $f(-1) = 2 \times (-1) + 5 = 3.$ Likewise if the input is 7 then the output is $f(7) = 2 \times 7 - 5 = 14 - 5 = 9.$

I hope this helps,


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