Use the graph of the function to answer each question. (−2𝜋 ≤ x ≤ 2𝜋) f(x) = cot(x)

Question

(a) Find all x-intercepts of the graph of y = f(x). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

X =

(c) Find the intervals on which the graph of y = f(x) is increasing and the intervals on which the graph of y = f(x) is decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

Increasing:

Decreasing:

(d) Find all relative extrema, if any, of the graph of y = f(x). (Enter your answers as a comma-separated list of ordered pairs. If an answer does not exist, enter DNE.)

Relative minima:

Relative maxima:

Answer 1

-3pi/2, -pi/2, pi/2, 3pi/2

4 x intercepts, no y intercepts

the graph is always decreasing,from left to right, always downward sloping. the slope is always negative

but

at -pi, 0, and pi, there are discontinuities, as the graph jumps from -infinity to plus infinity. In some sense, you might call that discontinuous jump in value a point of the graph where it is increasing in value

there are no local or relative maximums or minimums

the graph goes to infinity and negative infinity, no global max or min either