Question

determine the end behavior of the polynomial function:
$y = 3x^2 + x - 2$.

select one:
a. as $x \
ightarrow -\infty$, $f(x) \
ightarrow \infty$ and $x \
ightarrow \infty$, $f(x) \
ightarrow \infty$.
b. as $x \
ightarrow -\infty$, $f(x) \
ightarrow -\infty$ and $x \
ightarrow \infty$,
$f(x) \
ightarrow \infty$.
c. as $x \
ightarrow -\infty$, $f(x) \
ightarrow \infty$ and $x \
ightarrow \infty$,
$f(x) \
ightarrow -\infty$.
d. as $x \
ightarrow -\infty$, $f(x) \
ightarrow -\infty$ and $x \
ightarrow \infty$,
$f(x) \
ightarrow -\infty$.

Explanation:

Step1: Identify degree and leading coefficient

The polynomial is $y=3x^2+x-2$. Degree $n=2$ (even), leading coefficient $a=3$ (positive).

Step2: Apply end behavior rules

For even degree, $x\to\pm\infty$, $f(x)$ matches sign of $a$. Since $a>0$, $f(x)\to\infty$ in both directions.

Answer:

A. As $x \to -\infty$, $f(x) \to \infty$ and $x \to \infty$, $f(x) \to \infty$.