That is a function defined as:
f(x) = -1 if x is negative
f(x) = 0 if x is zero
f(x) = 1 if x is positive
In other words, a function that basically distinguishes whether the input is positive, negative, or zero.
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Honey, the signum function is about as bijective as a one-way street. It sure ain't bijective, because it maps every non-zero number to 1, completely ignoring the negative numbers. So, in short, signum function is not bijective, it's as one-sided as a bad Tinder date.
If y is an exponential function of x then x is a logarithmic function of y - so to change from an exponential function to a logarithmic function, change the subject of the function from one variable to the other.
Yes, the word 'function' is a noun (function, functions) as well as a verb (function, functions, functioning, functioned). Examples: Noun: The function of the receptionist is to greet visitors and answer incoming calls. Verb: You function as the intermediary between the public and the staff.
yes
That's true. If a function is continuous, it's (Riemman) integrable, but the converse is not true.