Find the net signed area between the graph of the function f(x)=3−|x+1| and the x-axis over the interval [−6,4]. Submit your answer as an exact value.

Answer 1

the area between f(x) = 3 - |x+1| and the x-axis over the interval [-6,4]

= 9 above the x axis and 4 below the x axis

9-4 = 5 = net area

or if the two areas are added, it's 9+4 = 13 total area

vertex is (-1,3). It's symmetric about x =-1

x intercepts are x= 2 and -4. The points (2,0) and (-4,0)

from x=-6 to x =-4 the curve is below the x axis with area = 2

from x=2 to x =4 the curve is below the x axis with area = 2

from x =-4 to x=2 the curve is above the x axis with area = 9

the graph has an inverted "V" shape. Maximum y value = 3, Minimum y value = 2 in the given interval