Question

Two friends decide to go on a four-hour ride on off-road vehicles through mountainous terrain. The graph represents their elevation (in hundreds of feet) as a function of time (in hours). The ride started 2,000 feet above sea level, so for the purposes of this problem, assume the x-axis represents an elevation of 2,000 feet.

Find the key features of the graph. That is, find the extrema, zeros, end behavior, increasing and decreasing intervals, and positive and negative intervals.

Answer 1

Extrema: relative minimum (1.25,-3.25), relative maximums (3.25,10) and (0,0)

Zeros: (0,0), (2,0), and (4,0)

End behavior: As x approaches infinity, the function approaches negative infinity. As x approaches negative infinity, the function approaches negative infinity.

Intervals of increase and decrease: increasing on (-∞, 0) and (1.25, 3.25), decreasing on (0, 1.25) and (3.25, ∞)

Positive and negative intervals: positive on (2, 4), negative on (-∞, 0), (0, 2), and (4, ∞)

Answer 2

The elevation is positive on the interval (2,4) .

The elevation reaches a relative maximum of about 1,000 feet above the starting point.

The domain of the function is 0<x<4 .

Explanation:

edmentum