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