Chapter 12.8, Problem 2GP

To determine

Find the amplitude, period and vertical shift for each function. Also, draw the graph of the function.

Answer to Problem 2GP

The amplitude, period and vertical shift of the function is $doesn\text{'}texist,\pi \&3unit\mathrm{s}up$ .

Explanation of Solution

Given: It is given in the question that the function is $y=\tan \theta +3$ .

Concept Used:

In this, use the concept of the general equation for tangent $y=a\tan b\theta +d$ , where a is amplitude which does not exist, $\frac{\pi }{\left|b\right|}$ is period and d is the vertical shift if d is positive it shifts to up and if it is negative , it shift to down.

Calculation: Here, the function is $y=\tan \theta +3$ .

In this, $a=1$ , but it is a tangent function so the amplitude does not exist.

Now, the value of b is $1$ , so the period is: $\frac{\pi }{\left|b\right|}=\frac{\pi }{1}=\pi$

From the equation it is find that d is $3$ with positive sign, so vertical shift is $3$ units up.

The graph of the function is given below:

  

Conclusion:

The amplitude, period and vertical shift are $doesn\text{'}texist,\pi \&3unit\mathrm{s}up$