Question

describe the end behavior (long run behavior) of $f(x)=x^{2}$
as $x\to -\infty, f(x)\to ?$
as $x\to \infty, f(x)\to ?$
question help: video

Explanation:

Step1: Analyze when $x\to -\infty$

When $x$ approaches negative infinity, $x^2=(-x)\times(-x)$. Since $-x$ approaches positive infinity as $x\to -\infty$, and the product of two large positive - valued numbers is large positive. So as $x\to -\infty$, $f(x)=x^2\to+\infty$.

Step2: Analyze when $x\to\infty$

When $x$ approaches positive infinity, $x^2 = x\times x$. The product of two large positive - valued numbers is large positive. So as $x\to\infty$, $f(x)=x^2\to+\infty$.

Answer:

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