Answer:
Function: Yes
A. Domain: [-π, π]
Range: [-1, 1]
B. y-intercept: (0, 0)
x-intercepts: (-π, 0), (0, 0), and (π, 0)
C. Symmetric about the origin
Explanation:
If we draw a vertical line and the line only crosses the graph once, we can say that the graph is a function. In this case, we get:
Then, we can say that the graph is a function. So, the answer is Yes.
Part A.
The domain is the set of values that the x-variable can take and the range is the set of values that the y-variable can take, so
Domain: [-π, π]
Range: [-1, 1]
Part B.
The intercepts are the points where the graph crosses the y-axis or the x-axis. Therefore
y-intercept: (0, 0)
x-intercepts: (-π, 0), (0, 0), and (π, 0)
Part C.
This figure is symmetric with respect to the origin because for each point in the second quadrant there is a point in the fourth quadrant.
Therefore, the answers are
Function: Yes
A. Domain: [-π, π]
Range: [-1, 1]
B. y-intercept: (0, 0)
x-intercepts: (-π, 0), (0, 0), and (π, 0)
C. Symmetric about the origin
