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 (a) what are the intercepts? (simplify your answer. type an ordered pair. use a comma to separate answers as needed. type an exact answer, using π as needed.) (b) the domain is (type your answer in interval notation. type an exact answer, using π as needed.) 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 boxes within your choice.

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 (a) what are the intercepts? (simplify your answer. type an ordered pair. use a comma to separate answers as needed. type an exact answer, using π as needed.) (b) the domain is (type your answer in interval notation. type an exact answer, using π as needed.) 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 boxes within your choice.

Answer

Explanation:

Step1: Find x - intercepts

The x - intercepts are the points where the graph crosses the x - axis. From the graph, the x - intercepts are $(-\pi,0)$ and $(\pi,0)$.

Step2: Find y - intercept

The y - intercept is the point where the graph crosses the y - axis. From the graph, the y - intercept is $(0,0)$.

Step3: Determine the domain

The domain is the set of all x - values of the function. From the graph, the domain is $[-\pi,\pi]$.

Step4: Determine the range

The range is the set of all y - values of the function. From the graph, the range is $[-9,9]$.

Step5: Find increasing intervals

The function is increasing when the y - values are getting larger as the x - values increase. The increasing intervals are $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$.

Step6: Find decreasing intervals

The function is decreasing when the y - values are getting smaller as the x - values increase. The decreasing intervals are $\left[-\pi,-\frac{\pi}{2}\right]$ and $\left[\frac{\pi}{2},\pi\right]$.

Step7: Check for even/odd function

A function $y = f(x)$ is even if $f(-x)=f(x)$ and odd if $f(-x)=-f(x)$. Since the graph is symmetric about the origin, $f(-x)=-f(x)$ and the function is odd.

Answer:

(a) $(-\pi,0),(0,0),(\pi,0)$ (b) Domain: $[-\pi,\pi]$, Range: $[-9,9]$ (c) Increasing interval: $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$, Decreasing intervals: $\left[-\pi,-\frac{\pi}{2}\right],\left[\frac{\pi}{2},\pi\right]$ (d) Odd