Chapter 14.4, Problem 24E

To determine

To Find: The equation for the secant function with the period of $\frac{\pi }{2}$ a phase shift of $-\pi$ and the vertical shift of $3$ .

Answer to Problem 24E

The required function is $y=3+\sec \left(4x+\frac{\pi }{2}\right)$ .

Explanation of Solution

Consider the general function is,

  $y=k+\sec \left(ax+b\right)$

Consider the period is $\frac{2\pi }{a}$ , the phase shift is b and vertical shift is k .

Since, the secant function have the period is $\frac{\pi }{2}$ phase shift $-\pi$ and the vertical shift 3 is,

  $y=3+\sec \left(4x+\frac{\pi }{2}\right)$