## mathmath333 one year ago State if $$f$$ is a function

1. mathmath333

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}}

2. anonymous

How would you begin?

3. anonymous

(What are the conditions for f being a function? )

4. mathmath333

idk

5. anonymous

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.

6. anonymous

So here you should look if there isn't a x-value with two different y-values

7. mathmath333

i didnt understand

8. anonymous

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

9. mathmath333

why for only x=3

10. uri

@mathmath333 why are you faking as tania sachdev?

11. mathmath333

i m not

12. anonymous

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

13. mathmath333

so it is same for x=3

14. anonymous

If they're the same, you have just one Y-value for the x-value, s it's a function