Question

determine the end behavior for the following function. as x → ∞, f(x) → -∞. as x → -∞, f(x) → ∞. as x → ∞, f(x) → ∞. as x → -∞, f(x) → ∞. as x → ∞, f(x) → ∞. as x → -∞, f(x) → -∞. as x → ∞, f(x) → -∞. as x → -∞, f(x) → -∞.

Explanation:

Step1: Observe right - hand end behavior

As \(x\) approaches positive infinity (\(x
ightarrow\infty\)), we look at the right - most part of the graph. The graph is going up, so \(f(x)
ightarrow\infty\).

Step2: Observe left - hand end behavior

As \(x\) approaches negative infinity (\(x
ightarrow-\infty\)), we look at the left - most part of the graph. The graph is going up, so \(f(x)
ightarrow\infty\).

Answer:

As \(x
ightarrow\infty\), \(f(x)
ightarrow\infty\). As \(x
ightarrow-\infty\), \(f(x)
ightarrow\infty\).