# How do you graph y=secx+2?

Jun 14, 2018

#### Explanation:

Given: $y = \sec x + 2$

First draw a dashed vertical shift line at $y = 2$

Since $\sec x = \frac{1}{\cos x}$, sketch a dashed cosine function

$y = \cos x + 2 \implies \text{ amplitude" = 1 " and period } = 2 \pi$

Remember that a cosine with a period of $2 \pi$ needs to be divided into 4 sections: $0 , \frac{\pi}{2} , \pi , \frac{3 \pi}{2} , 2 \pi$.

Wherever the cosine function crosses the $y = 2$ line there will be a vertical asymptote. At each peak and trough, there will be a point on the secant function that arcs up to the adjacent vertical asymptotes: