31: f is continuous on its domain
f (x + 2kπ) = f (x),
hence f is
2π-periodic.
y-intercept: f (0) not possible;
x-intercepts: f = 0 gives
x = π/2 + 2kπ.
f is not symmetric since D( f ) is not
symmetric.
Limits at endpoints:
Limit at minus infinity and infinity not possible since
D( f ) does not contain any neighborhoods of these
points.
Interpretation as asymptotes:
Vertical asymptote at
x = 2kπ.
Vertical asymptote at
x = (2k + 1)π.
Now determine monotonicity using f ′.
Next hint
Answer