eves teacher asked her to graph the function (y = -cot(x)-1) by reflecting the graph of the function (y =…

eves teacher asked her to graph the function (y = -cot(x)-1) by reflecting the graph of the function (y = cot(x)) about the x - axis and translating it vertically. does it matter in which order eve does the transformations?\nyes, it matters. the graph of the function (y = cot(x)) should be reflected about the x - axis before it is translated 1 unit down.\nyes, it matters. the graph of the function (y = cot(x)) should be reflected about the x - axis before it is translated 1 unit up.\nno, it doesnt matter. reflecting the graph of the function (y = cot(x)) about the x - axis and translating the graph 1 unit down in either order will produce the correct graph.\nno, it doesnt matter. reflecting the graph of the function (y = cot(x)) about the x - axis and translating the graph 1 unit up in either order will produce the correct graph.

eves teacher asked her to graph the function (y = -cot(x)-1) by reflecting the graph of the function (y = cot(x)) about the x - axis and translating it vertically. does it matter in which order eve does the transformations?\nyes, it matters. the graph of the function (y = cot(x)) should be reflected about the x - axis before it is translated 1 unit down.\nyes, it matters. the graph of the function (y = cot(x)) should be reflected about the x - axis before it is translated 1 unit up.\nno, it doesnt matter. reflecting the graph of the function (y = cot(x)) about the x - axis and translating the graph 1 unit down in either order will produce the correct graph.\nno, it doesnt matter. reflecting the graph of the function (y = cot(x)) about the x - axis and translating the graph 1 unit up in either order will produce the correct graph.

Answer

Explanation:

Step1: Define the two transformations

Let (f(x)=\cot(x)). Reflection about the (x -)axis gives (y = - f(x)=-\cot(x)). Vertical translation of (y = f(x)) by (k) units gives (y=f(x)+k). Here (k=- 1) for a translation 1 unit down.

Step2: First, reflect then translate

If we first reflect (y = \cot(x)) about the (x -)axis, we get (y=-\cot(x)). Then translating 1 unit down gives (y =-\cot(x)-1).

Step3: First, translate then reflect

If we first translate (y=\cot(x)) 1 unit down, we get (y=\cot(x)-1). Then reflecting about the (x -)axis gives (y=-(\cot(x) - 1)=-\cot(x)+1\neq-\cot(x)-1). The correct vertical - translation is 1 unit down. If we first reflect (y = \cot(x)) about the (x -)axis to get (y =-\cot(x)) and then translate 1 unit down, we get (y=-\cot(x)-1). Also, if we first translate (y = \cot(x)) 1 unit down to get (y=\cot(x)-1) and then reflect about the (x -)axis we get (y=-(\cot(x)-1)=-\cot(x) + 1\neq-\cot(x)-1). The correct order is to reflect about the (x -)axis first and then translate 1 unit down.

Answer:

Yes, it matters. The graph of the function (y = \cot(x)) should be reflected about the (x - )axis before it is translated 1 unit down.