Question

A population of coyotes is known to show periodic behavior over time. The table shows the population of coyotes in a specific area over time.

Answer 1

Answer:

$\cot x$

Step-by-step explanation:

It is required to find the parent function of the given graph.

Since, we know that,

Range of the functions, $\sin x$ and $\cos x$ is [-1,1].

So, the given graph cannot be obtained from the functions $\sin x$ and $\cos x$.

Also, we know,

Range of the functions, $\csc x$ and $\sec x$ is $(-\infty,-1]\cup [1,\infty)$.

Thus, the given graph cannot be obtained from the functions $\csc x$ and $\sec x$.

So, we are left with the functions, $\tan x$ and $\cot x$.

Moreover, as $\tan 0=0$

But, in the graph, function is going to infinity when x= 0.

Thus, the graph cannot be obtained from $\tan x$.

Hence, the parent function is $\cot x$.