describe the end behavior of the function x→∞,f(x)→2 and x→−∞, f(x)→∞ x→∞, f(x)→∞ and x→−∞, f(x)→∞ x→∞…

Explanation:

Step1: Analyze right - hand end behavior

As (x\to\infty), we look at the trend of the function on the right - hand side of the graph. If the function approaches a horizontal line (y = L), then (\lim_{x\to\infty}f(x)=L). If it goes up or down without bound, (\lim_{x\to\infty}f(x)=\pm\infty).

Step2: Analyze left - hand end behavior

As (x\to-\infty), we look at the trend of the function on the left - hand side of the graph. If the function approaches a horizontal line (y = L), then (\lim_{x\to-\infty}f(x)=L). If it goes up or down without bound, (\lim_{x\to-\infty}f(x)=\pm\infty).

Step3: Match with options

By observing the graph, as (x\to\infty), (f(x)\to2) and as (x\to-\infty), (f(x)\to\infty).

Answer:

x →∞,f(x)→2 and x→ -∞, f(x)→∞