Question

Excuse the quality of my picture. I am trying to find which piecewise functions are represented by this graph.

Answer 1

Let's begin with the line that goes from minus infinity to zero

the equation of this line is

$y=x+2$

because of the filled circle we know that this interval touch the zero

$(-\infty,0\rbrack$

in inequality, this will be

$x\le0$

then for the line that is between 0 and 2, we have a filled circle in the number two therefore we can touch this number

the interval will be

$(0,2\rbrack$

in inequality notation

$0 for the line that starts in 2 we have an empty

the interval

[tex](2,\infty)$

in inequality notation

$x>2$

Therefore the piecewise function i

$f(x)=f(x)=\begin{cases}x+2,ifx\le0 \\ \frac{x}{3}+1,if02\end{cases}$

the correct option is the second one