The graph below shows the height of a tunnel f(x), in feet, depending on the distance from one side of the tunnel x, in feet. (graph attached)

part a: what do the x-intercepts and maximum value of the graph represent? what are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height?

part b: what is an approximate average rate of change of the graph from x=15 to x=35, and what does this rate represent?

Part A:

The x-intercept represents the point where each side of the tunnel meets the ground. The first point is at x = 0 and the second is at x = 100 (each square is going up in 10s)

The maximum point represents the highest point of the tunnel.

The function reaches its maximum point before it decreases again in between x = 40 and x = 60

At x = 40 and x= 60, the height of the tunnel is y = 47. Translating this into the context means that at the distance of 40 units and 60 units from the point 0, the height of the tunnel is 47 units

Part B:

When x = 15, y = 25
When x = 35, y = 45

The rate of change is represented by the slope ⇒ 
(45 - 25) ÷ (35 - 15) = 20÷20 = 1 
It means that for every one unit of distance, the height increase by one unit.