Explanation:
The reciprocal function of y = f(x) is the function y = 1/f(x)
So, to graph the reciprocal function, we need to identify the values of y for some points in the graph.
For example, y is equal to 0 at x = 0, x = 2π, and x = -2π.
It means that at x = 0, x = 2π, and x = -2π, the reciprocal function will be
1/f(x) = 1/0
Since the division by 0 is not defined, there will be vertical asymtotes at x = 0, x = 2π, and x = -2π.
On the other hand, we can see that at x = π and x = -3π, y is equal to 0.5, so the reciprocal function will be equal to:
1/f(x) = 1/0.5 = 2
And at x = -π and x = 3π, y is equal to -0.5, so the reciprocal function will be equal to:
1/f(x) = 1/(-0.5) = - 2
Therefore, we have the following for the reciprocal function:
It passes through the points (π, 2), (-3π, 2), (-π, -2), and (3π, -2)
It has vertical asymptotes in x = 0, x = 2π and x = -2π
So, the graph is:
