This section discusses the graph of the secant function (shown below).
For ease of reference, some material is repeated
from the Trigonometric Functions.
$\displaystyle y = \sec x := \frac{1}{\cos x}$ (periodic with period $\,2\pi\,$) The cosine curve is shown in red. 

Key ideas contributing to the graph:

The graph of the secant function is easy to obtain as the reciprocal of the
cosine function.
The key ideas are illuminated below:
the reciprocal of $\,1\,$ is $\,1\,$, so the points shown do not move 
the reciprocal of $\,1\,$ is $\,1\,$, so the points shown do not move 
zero has no reciprocal: where the cosine is zero, the secant has a vertical asymptote 
the reciprocal of a small positive number is a large positive number 
the reciprocal of a small negative number is a large negative number 
the cosine curve is bounded between $\,\color{red}{1}\,$ and $\,\color{red}{1}\,$; thus, the reciprocals all have size greater than or equal to $\,\color{green}{1}\,$ 
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
PROBLEM TYPES:
