using the given graph of the function f, find the following. (a) the intercepts, if any (b) its domain and…

using the given graph of the function f, find the following. (a) the intercepts, if any (b) its domain and range (c) the intervals on which it is increasing, decreasing, or constant (d) whether it is even, odd, or neither the range is . (type your answer in interval notation. type an exact answer, using π as needed.) (c) on which interval(s) is the graph increasing? select the correct choice below and fill in any
Answer
Explanation:
Step1: Identify range from graph
The lowest - y value is - 6 and the highest is 6.
Step2: Write in interval notation
The range is all y - values between - 6 and 6 inclusive. So the range is $[-6,6]$.
Step3: Identify increasing intervals
The function is increasing when the graph goes up as we move from left to right. From the graph, it is increasing on the interval $\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$.
Answer:
(a) x - intercepts: $x =-\pi,0,\pi$; y - intercept: $y = 0$ (b) Domain: $[-\pi,\pi]$, Range: $[-6,6]$ (c) Increasing interval: $\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$ (d) The function is odd since it is symmetric about the origin.