Let $$f: \mathbb{R} \to \mathbb{R}$$ be defined as $$f(x) = \dfrac{2x^2 - 3x + 2}{3x^2 + x + 3}$$. Then $$f$$ is :

$$\lim_{x \to \pm\infty} f(x) = \lim_{x \to \pm\infty} \frac{2x^2 - 3x + 2}{3x^2 + x + 3}$$

$$\lim_{x \to \pm\infty} \frac{2 - \frac{3}{x} + \frac{2}{x^2}}{3 + \frac{1}{x} + \frac{3}{x^2}} = \frac{2}{3}$$

Because the Range is a restricted subset of $$\mathbb{R}$$ (bounded interval) and does not equal the codomain $$\mathbb{R}$$, $$f(x)$$ is not onto.

Since $$\lim_{x \to -\infty} f(x) = \frac{2}{3}$$ and $$\lim_{x \to \infty} f(x) = \frac{2}{3}$$, a continuous function that starts and ends at the same horizontal asymptotic line must turn around at least once (possess local extrema). Therefore, $$f(x)$$ is not one-one.