the piecewise defined function f(x) is graphed below. what is the value of f(5)?\noptions:\n- f(5) = -1\n…

Explanation:

Step1: Analyze the graph's points at x=5

To find ( f(5) ), we look at the graph of the piecewise function at ( x = 5 ). In a piecewise function's graph, a solid dot (filled circle) indicates the function's value at that point, while an open dot (hollow circle) does not. At ( x = 5 ), the solid dot is at ( (5, -1) ), and the open dot is at ( (5, 3) ). The solid dot represents the actual value of the function at ( x = 5 ).

Step2: Determine ( f(5) )

Since the solid dot at ( x = 5 ) is at ( (5, -1) ), this means the ( y )-value (which is ( f(x) )) when ( x = 5 ) is ( -1 ). So ( f(5) = -1 ).

Answer:

( f(5) = -1 ) (corresponding to the option: ( f(5) = -1 ))