The graph is a piecewise linear function with two segments: y=x for x<50 and y=80 for x>50. The function intersects y=50 at x=50, y=80 at x=88 and y=0 at x=-40.
The graph shows a piecewise linear function with two segments. The first segment has a slope of 1 and a y-intercept of 0, so it is a line equation of
. The second segment has a slope of 0 and a y-intercept of 80, so it is a line equation of
.
To answer the parts (a)-(f), we need to find the x-values where the graph intersects the lines
and
.
(a) The graph intersects the line y=50 at x=50. So, the solution to f(x)=50 is x=boxed{50}.
(b) The graph intersects the line
. So, the solution to f{x)=80 is x=boxed{88}.
(c) The graph intersects the line y=0 at x=-40. So, the solution to f(x)=0 is x=boxed{-40}.
(d) The graph is above the line y=50 between x=50 and x=88. So, the solution to f(x)>50 is xinboxed{(50,88)}.
(e) The graph is below or equal to the line y=80 between x=-40 and x=88. So, the solution to f(x)80 is xinboxed{[-40,88]}.
(f) The graph is between the lines y=0 and y=80 between x=-40 and x=88. So, the solution to 0<f(x)<80 is xinboxed{(-40,88)}.