Problem 1 the graph of a function f is shown Use the graph t

Problem 1 the graph of a function f is shown. Use the graph to find f^-1 (6).

Problem 2 Determine the intervals of the domain over which the given function is increasing, decreasing, and constant.

Solution

1. From the graph, it is apparent that it is a piecewise function. Since we need to determine f ^-1(6). Since f(8) = 6, therefore f ^-1(6) = 8.

2. The given function is increasing over the interval ( - , -3] as the graph is rising in this interval.

  The given function is decreasing over the interval [4, ) as the graph is falling in this interval.

The given function is constant over the interval (-3, 4) as the graph is flat in this interval. ( There are holes at both the ends, hence open intervals)