Let's analyze the given graph to answer each of the questions:

(a) Intercepts

Intercepts are the points where the graph crosses the x-axis (x-intercepts) and y-axis (y-intercepts).

• X-intercepts: The graph crosses the x-axis at $x = -\frac{\pi}{2}$, $x = 0$, and $x = \frac{\pi}{2}$.
• Y-intercept: The graph crosses the y-axis at $y = 0$ when $x = 0$.

(b) Domain and Range

• Domain: The set of all possible $x$-values for the function. Based on the graph, the domain is $[-\pi, \pi]$.
• Range: The set of all possible $y$-values for the function. From the graph, the range is $[-1, 1]$.

(c) Intervals of Increase, Decrease, and Constant

• The function is increasing on the interval $\left(-\pi, -\frac{\pi}{2}\right)$ and $\left(0, \frac{\pi}{2}\right)$.
• The function is decreasing on the interval $\left(-\frac{\pi}{2}, 0\right)$ and $\left(\frac{\pi}{2}, \pi\right)$.
• There are no intervals where the function is constant.

(d) Even, Odd, or Neither

• To determine if the function is even, odd, or neither, we can observe its symmetry.
  • A function is even if it is symmetric with respect to the y-axis: $f(x) = f(-x)$.
  • A function is odd if it is symmetric with respect to the origin: $f(-x) = -f(x)$.

Based on the graph, the function appears to be odd, as it has origin symmetry.

Would you like more details or have any questions?

Related Questions

1. How can you determine the intervals of concavity from a graph?
2. What are some characteristics of even and odd functions?
3. How do you find intercepts algebraically from a function's equation?
4. What does the derivative tell you about increasing and decreasing intervals?
5. How can you find the maximum and minimum points using calculus?

Tip

When analyzing graphs, symmetry is a quick way to identify whether a function is even, odd, or neither!