identifying a negative interval using a graph\nwhich function is negative for the interval -1, 1?

Answer:

We need to visually inspect each graph to see which one has (y - values) less than (0) (negative) for all (x) - values in the interval ([-1,1]).

1. For the first graph:
   • When (x\in[-1,1]), the (y) - values are negative.
2. For the second graph:
   • When (x = 0), (y= - 2), but when (x=\pm1), (y = 0), so it is not negative for the entire interval ([-1,1]).
3. For the third graph:
   • When (x\in[-1,1]), the (y) - values are non - negative ( (y\geq0)).
4. For the fourth graph:
   • When (x\in[-1,1]), the (y) - values are non - negative ( (y\geq0)).

So the function represented by the first graph is negative for the interval ([-1,1]).

Explanation:

Step1: Analyze first graph

Check (y) values in ([-1,1]). All (y<0).

Step2: Analyze second graph

At (x = \pm1), (y = 0), not negative throughout.

Step3: Analyze third graph

All (y\geq0) in ([-1,1]).

Step4: Analyze fourth graph

All (y\geq0) in ([-1,1]).