Question

PLEASE HELP!!!
What is the end behavior of the function?

Answer 1

`\textsf{D)}\quad \begin{array}{l}\textsf{As}\;x \rightarrow \infty, f(x) \rightarrow \infty\\\\\textsf{As}\;x \rightarrow -\infty, f(x) \rightarrow \infty\end{array}`

Explanation:

The end behavior of a function describes how the function behaves as the independent variable (x-value) approaches positive or negative infinity, indicating the long-term trends of the function's values.

Given function:

`f(x)=(5)/(4)x^2`

Since the square of a number is always non-negative:

• As x approaches positive infinity (+∞), the function f(x) also approaches positive infinity (+∞). In other words, the function grows without bound as x becomes very large on the positive side.
• As x approaches negative infinity (-∞), the function f(x) also approaches positive infinity (+∞). Similarly, on the negative side, the function grows without bound.

Therefore, the end behavior of the function is:

`\boxed{\begin{array}{l}\textsf{As}\;x \rightarrow \infty, f(x) \rightarrow \infty\\\\\textsf{As}\;x \rightarrow -\infty, f(x) \rightarrow \infty\end{array}}`