Question

Which of the following is the graph of the piecewise function? Thanks for your help!

Answer 1

Thus this is the answer. The second graph from top to bottom.

1) The first thing to analyze on the Piecewise functions are the intervals, and how the function behaves accordingly.

2) So, in this question for x is greater than or equal to zero, there is an exponential function and for all positive numbers, there is a rational equation.

`f(x)=\left\{\begin{matrix} e^(-x),x\leq 0\\(x^(2)+5x+6)/(x^(2)+2x-3),x>0\end{matrix}\right.`

3) So, we can plot the following for that:

Thus this is the answer. The second graph is from top to bottom.