question 7\ngive an equation for the function whose graph appears above. there are, of course, infinitely…

question 7\ngive an equation for the function whose graph appears above. there are, of course, infinitely many answers, but it is possible to write the answer in the form d + atan(x) or d + acot(x). watch the video if you are stuck!\nf(x) =\nquestion help: video\nsubmit question

question 7\ngive an equation for the function whose graph appears above. there are, of course, infinitely many answers, but it is possible to write the answer in the form d + atan(x) or d + acot(x). watch the video if you are stuck!\nf(x) =\nquestion help: video\nsubmit question

Answer

Explanation:

Step1: Identify the general form

The general form of the function is $y = D+A\tan(x)$ or $y = D + A\cot(x)$. The graph has vertical - asymptotes and a shape similar to the tangent function, so we use $y = D+A\tan(x)$.

Step2: Determine the vertical shift $D$

The graph is shifted up. When $x = 0$, $y = 2$. For the function $y = D+A\tan(x)$, when $x = 0$, $\tan(0)=0$. So $D = 2$.

Step3: Determine the amplitude $A$

The basic tangent function $y=\tan(x)$ has a period of $\pi$ and passes through the origin. Our function $y = D+A\tan(x)$ has the same period as $y = \tan(x)$ (since there is no horizontal stretch/compression). The shape of the graph is not vertically stretched or compressed in an unusual way compared to the basic tangent function, so $A = 1$.

Answer:

$f(x)=2 + \tan(x)$