Using the given graph of the function f find the following t

Using the given graph of the function f, find the following. the intercepts, if any its domain and range the intervals on which it is increasing, decreasing, or constant whether it is even, odd, or neither

Solution

The given graph crosses both the X- Axis and the Y- Axis at the point ( 0,5). Thus

( a) The y –intercept is 0. The x –intercept is 5.

(b) The domain is ( -4, 2). The range is [ -1, 9]

(c ) The function is incresing on the interval ( 0,2). The function is decreasing on the interval ( -4, 0). The function is constant at x = 0.

( d) A function f is even if the graph of f is symmetric with respect to the y-axis. Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f. A function f is odd if the graph of f is symmetric with respect to the origin. Algebraically, f is odd if and only if f(-x) = -f(x) for all x in the domain of f. Here, the function is neither even nor odd ( f (1) = 7 whereas f ( -1) < 5 ).