Question

3
f(x) = 3x⁴ + 2x² + x + 7
orange
as x → -∞, f(x) → ∞
as x → ∞, f(x) → ∞
red
as x → -∞, f(x) → -∞
as x → ∞, f(x) → ∞
yellow
as x → -∞, f(x) → ∞
as x → ∞, f(x) → -∞
white
as x → -∞, f(x) → -∞
as x → ∞, f(x) → -∞

Explanation:

Step1: Identify degree and leading coefficient

The function $f(x)=3x^4+2x^2+x+7$ has degree $4$ (even) and leading coefficient $3>0$.

Step2: Analyze end behavior

For even degree with positive leading coefficient:
As $x \to -\infty$, $x^4 \to \infty$, so $f(x)=3x^4+\dots \to \infty$.
As $x \to \infty$, $x^4 \to \infty$, so $f(x)=3x^4+\dots \to \infty$.

Answer:

ORANGE: as $x \to -\infty, f(x) \to \infty$; as $x \to \infty, f(x) \to \infty$