Answer
(a) See graph.
(b) domain $(-\infty,\infty)$ and range $[-\frac{7}{3},\infty)$.
(c) increasing on $(-\frac{2}{3},\infty)$ and decreasing on $(-\infty,-\frac{2}{3})$.
Work Step by Step
(a) Given $f(x)=3x^2+4x-1=3(x+\frac{2}{3})^2-\frac{7}{3}$ with $a=3\gt0$, thus its graph opens up, its vertex is $(-\frac{2}{3},-\frac{7}{3})$, axis of symmetry is $x=-\frac{2}{3}$, y-intercept is $(0,-1)$ (let x=0), and x-intercepts are $(-\frac{2}{3}\pm\frac{\sqrt 7}{3},0)$ (let f=0). See graph.
(b) Based on the graph, we can find the domain $(-\infty,\infty)$ and range $[-\frac{7}{3},\infty)$.
(c) Based on the graph, we can find the function is increasing on $(-\frac{2}{3},\infty)$ and decreasing on $(-\infty,-\frac{2}{3})$.
