which function is positive for the entire interval -3,-2?

Explanation:

Step1: Analyze function values on interval

Check the y - values of each function on the interval $[-3,-2]$. A function is positive when its $y>0$ for all $x$ in the given interval.

Step2: Examine first graph

For the first graph, when $x\in[-3,-2]$, the $y$ - values are negative.

Step3: Examine second graph

For the second graph, when $x\in[-3,-2]$, the $y$ - values are negative.

Step4: Examine third graph

For the third graph, when $x\in[-3,-2]$, the $y$ - values are positive.

Step5: Examine fourth graph

For the fourth graph, when $x\in[-3,-2]$, the $y$ - values are negative.

Answer:

The third function (the one with positive $y$ - values on the interval $[-3,-2]$)