Question

When graphing the function f(x)=-|x+5|+12 on your graphing calculator, what is the most appropriate viewing window for determining the domain and range of the function?
Xmin: –10, Xmax: 10
Ymin: –10, Ymax: 10
Xmin: –20, Xmax: 20
Ymin: –20, Ymax: 20
Xmin: –5, Xmax: 5
Ymin: –20, Ymax: 20
Xmin: –10, Xmax: 10
Ymin: –5, Ymax: 5

Answer 1

Choose Xmin = -20, Xmax = 20, Ymin = -20, Ymax = 20.

Reason: the vertex is at (-5, 12) (maximum 12), so the window must include y = 12; this window shows the vertex and the graph decreasing on both sides. From the graph (and algebra) domain = (-∞, ∞) and range = (-∞, 12].