Question

What is the end behavior of the function f(x) = 1/2x^2

Answer 1

We are given the function:

$f(x)\text{ = }\frac{1}{2}x^2$

The end behavior of a function describes the behavior of a function as x approaches positive infinity and as x approaches negative infinity.

To visualize the end behavior, we should plot the graph of the function. The graph is shown below:

We notice that:

$As\text{ x }\rightarrow+\infty,f(x)\rightarrow+\infty_{}$

and

$As\text{ x }\rightarrow-\infty,f(x)\rightarrow+\infty_{}$

Answer:

$\begin{gathered} As\text{ x }\rightarrow+\infty,f(x)\rightarrow+\infty_{} \\ As\text{ x }\rightarrow-\infty,f(x)\rightarrow+\infty_{} \end{gathered}$