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: f(x) = -|x+5| + 12 has vertex at (-5, 12) (the maximum) and opens downward. That window shows the vertex (y = 12) and the arms trending downward, so you can see the maximum and that the graph extends downwards. From the graph you can conclude domain = (−∞, ∞) and range = (−∞, 12].