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<p></p><p>the interval </p><p></p>[tex](2,\infty)`

in inequality notation

`x>2`

Therefore the piecewise function i

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

the correct option is the second one