Answer
(a) See graph.
(b) domain $(-\infty,\infty)$, range $[\frac{7}{8},\infty)$.
(c) increasing on $(-\frac{1}{4},\infty)$ and decreasing on $(-\infty,-\frac{1}{4})$.
Work Step by Step
(a) See graph for $f(x)=2x^2+x+1=2(x+\frac{1}{4})^2+\frac{7}{8}$ with vertex $(-\frac{1}{4},\frac{7}{8})$ and intercept $(0,1)$.
(b) We can determine the domain as $(-\infty,\infty)$ and the range as $[\frac{7}{8},\infty)$.
(c) We can determine the function is increasing on $(-\frac{1}{4},\infty)$ and decreasing on $(-\infty,-\frac{1}{4})$.
