State if \(f\) is a function

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State if \(f\) is a function

Mathematics
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A relation \(f\) is defined by \(\large \color{black}{\begin{align} f(x) = \begin{cases} x^2, & 0\leq x\leq 3 \\ 3x, & 3\leq x\leq 10 \end{cases}\hspace{.33em}\\~\\ \end{align}}\)
How would you begin?
(What are the conditions for f being a function? )

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idk
Actually, it's a rule that for f being a function, there could only be 1 Y-value per x-value. So in every x, the function could be unexisting or it could have 1 y-value.
So here you should look if there isn't a x-value with two different y-values
i didnt understand
You should look, if for x=3, if there are 2 different y-values. If there aren't two different values, it is a function
why for only x=3
  • uri
@mathmath333 why are you faking as tania sachdev?
i m not
In this case, you should only look at the case for x=3 because the two parts are both functions, the only problem could be, with the chosen intervals that for x=3 (in this case) the y-value of the first function is different from the second
so it is same for x=3
If they're the same, you have just one Y-value for the x-value, s it's a function

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