Question

describe the end behavior (long run behavior) of $f(x)=x^2$
as $x\to -\infty$, $f(x)\to ?$
as $x\to \infty$, $f(x)\to ?$
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Explanation:

Step1: Analyze \( x \to -\infty \)

For \( f(x) = x^2 \), when \( x \) is a large negative number (approaching \( -\infty \)), squaring it (multiplying a negative number by itself) gives a large positive number. So as \( x \to -\infty \), \( f(x) \to \infty \).

Step2: Analyze \( x \to \infty \)

When \( x \) is a large positive number (approaching \( \infty \)), squaring it also gives a large positive number. So as \( x \to \infty \), \( f(x) \to \infty \).

Answer:

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