Question

State if \(f\) is a function

Answer 1

A relation \(f\) is defined by

\(\large \color{black}{\begin{align} f(x) =
\begin{cases}
x^2, & 0\leq x\leq 3 \\
3x, & 3\leq x\leq 10
\end{cases}\hspace{.33em}\\~\\
\end{align}}\)

Answer 2

How would you begin?

Answer 3

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

Answer 4

idk

Answer 5

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.

Answer 6

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

Answer 7

i didnt understand

Answer 8

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

Answer 9

why for only x=3

Answer 10

@mathmath333 why are you faking as tania sachdev?

Answer 11

i m not

Answer 12

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

Answer 13

so it is same for x=3

Answer 14

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