based on the table, which best predicts the end behavior of the graph of f(x)?\nas x→∞, f(x)→∞, and as x→−∞…

based on the table, which best predicts the end behavior of the graph of f(x)?\nas x→∞, f(x)→∞, and as x→−∞, f(x)→∞.\nas x→∞, f(x)→∞, and as x→−∞, f(x)→−∞.\nas x→∞, f(x)→−∞, and as x→−∞, f(x)→∞.\nas x→∞, f(x)→−∞, and as x→−∞, f(x)→−∞.\n\nx\tf(x)\n-5\t-6\n-4\t-2\n-3\t0\n-2\t4\n-1\t4\n0\t0\n1\t-2\n2\t-6\n3\t-10

based on the table, which best predicts the end behavior of the graph of f(x)?\nas x→∞, f(x)→∞, and as x→−∞, f(x)→∞.\nas x→∞, f(x)→∞, and as x→−∞, f(x)→−∞.\nas x→∞, f(x)→−∞, and as x→−∞, f(x)→∞.\nas x→∞, f(x)→−∞, and as x→−∞, f(x)→−∞.\n\nx\tf(x)\n-5\t-6\n-4\t-2\n-3\t0\n-2\t4\n-1\t4\n0\t0\n1\t-2\n2\t-6\n3\t-10

Answer

Explanation:

Step1: Analyze x - values approaching negative infinity

As (x) decreases from (-5) to (-4,-3,-2,-1), (f(x)) first increases from (-6) to (-2), then to (0), (4), (4). As (x) continues to decrease further (towards (-\infty)), we can observe the general trend of the function values increasing. So as (x\to-\infty), (f(x)\to\infty).

Step2: Analyze x - values approaching positive infinity

As (x) increases from (0) to (1,2,3), (f(x)) decreases from (0) to (-2), (-6), (-10). As (x) continues to increase further (towards (\infty)), we can observe the general trend of the function values decreasing. So as (x\to\infty), (f(x)\to-\infty).

Answer:

As (x\to\infty), (f(x)\to-\infty), and as (x\to-\infty), (f(x)\to\infty)