Question

determine the end behaviors for the function ( f(x) ) graphed below.
left hand end behavior: as ( square
ightarrow square, square
ightarrow square )
right hand end behavior: as ( square
ightarrow square, square
ightarrow square )
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Explanation:

Step1: Analyze the left - hand end behavior

As \(x\) approaches \(-\infty\) (left - hand side), we look at the trend of the \(y\) - values. From the graph, as \(x\to-\infty\), \(y = f(x)\to-\infty\).

Step2: Analyze the right - hand end behavior

As \(x\) approaches \(\infty\) (right - hand side), we look at the trend of the \(y\) - values. From the graph, as \(x\to\infty\), \(y = f(x)\to-\infty\).

Answer:

Left hand end behavior: As \(x\to-\infty\), \(f(x)\to-\infty\)
Right hand end behavior: As \(x\to\infty\), \(f(x)\to-\infty\)