Answer:
[tex]\cot x[/tex]
Step-by-step explanation:
It is required to find the parent function of the given graph.
Since, we know that,
Range of the functions, [tex]\sin x[/tex] and [tex]\cos x[/tex] is [-1,1].
So, the given graph cannot be obtained from the functions [tex]\sin x[/tex] and [tex]\cos x[/tex].
Also, we know,
Range of the functions, [tex]\csc x[/tex] and [tex]\sec x[/tex] is [tex](-\infty,-1]\cup [1,\infty)[/tex].
Thus, the given graph cannot be obtained from the functions [tex]\csc x[/tex] and [tex]\sec x[/tex].
So, we are left with the functions, [tex]\tan x[/tex] and [tex]\cot x[/tex].
Moreover, as [tex]\tan 0=0[/tex]
But, in the graph, function is going to infinity when x= 0.
Thus, the graph cannot be obtained from [tex]\tan x[/tex].
Hence, the parent function is [tex]\cot x[/tex].
