Chapter 13.8, Problem 39PPS

To determine

Find the equation by using the given terms.

Answer to Problem 39PPS

The equation is $y=\tan (x-\pi )+2.5$ .

Explanation of Solution

Given: It is given in the question that the base equation is $y=\tan x$ and $\pi$ units to the right and $2.5$ units up.

Concept Used:

In this, use the concept of general equation for tangent $y=\tan (\theta -h)+d$ where h is phase shift and d is vertical shift and h units to the right if h is positive or h units to the left if h is negative.

Calculation: Here, let the equation be $y=\tan (\theta -h)+d$ .

Since, in this the phase shift is $\pi$ units to the right, so $h=\pi$ .

And the vertical shift d units up if d is positive or d down if d is negative.

In this, case the vertical shift is $2.5$ units up, so $d=2.5$ .

So, from the above put the values in the equation,

  $y=\tan (x-\pi )+2.5$ .

Conclusion:

The equation is $y=\tan (x-\pi )+2.5$ .