Question

based on the table, which best predicts the end behavior of the graph of ( f(x) )? as ( x
ightarrowinfty,f(x)
ightarrowinfty ), and as ( x
ightarrow-infty,f(x)
ightarrowinfty ). as ( x
ightarrowinfty,f(x)
ightarrowinfty ), and as ( x
ightarrow-infty,f(x)
ightarrow-infty ). as ( x
ightarrowinfty,f(x)
ightarrow-infty ), and as ( x
ightarrow-infty,f(x)
ightarrowinfty ). as ( x
ightarrowinfty,f(x)
ightarrow-infty ), and as ( x
ightarrow-infty,f(x)
ightarrow-infty ).

Explanation:

Step1: 分析函数值变化趋势

观察表格中\(x\)增大时\(f(x)\)的变化，当\(x\)从\(-5\)逐渐增大到\(3\)，\(f(x)\)的值先从\(-6\)上升到\(4\)（\(x=-2\)和\(x = -1\)时），然后又下降，且当\(x\)较大（如\(x = 3\)）时\(f(x)=-10\)，呈现出随着\(x\to+\infty\)，\(f(x)\to-\infty\)的趋势。

Step2: 分析\(x\to-\infty\)时函数值变化趋势

再看\(x\)减小（\(x\to-\infty\)方向），当\(x=-5\)时\(f(x)=-6\)，\(x=-4\)时\(f(x)=-2\)，\(x=-3\)时\(f(x)=0\)，整体呈现\(x\to-\infty\)时，\(f(x)\to+\infty\)的趋势。

Answer:

As \(x\to+\infty\)，\(f(x)\to-\infty\)，and as \(x\to-\infty\)，\(f(x)\to+\infty\)，so the answer is “As \(x\to+\infty\)，\(f(x)\to-\infty\)，and as \(x\to-\infty\)，\(f(x)\to+\infty\)”（即选项“As \(x\to+\infty\)，\(f(x)\to-\infty\)，and as \(x\to-\infty\)，\(f(x)\to+\infty\)”）。