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

`\cot x`

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`.