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

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?\no 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.\no yes, it matters. the graph of the function $y=cot(x)$ should be reflected about the $x$-axis before it is translated 1 unit up.\no no, 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.\no no, 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?\no 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.\no yes, it matters. the graph of the function $y=cot(x)$ should be reflected about the $x$-axis before it is translated 1 unit up.\no no, 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.\no no, 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: Analyze reflection

Reflecting $y = \cot(x)$ about the $x$-axis gives $y=-\cot(x)$.

Step2: Analyze translation

Translating $y = -\cot(x)$ 1 unit down gives $y=-\cot(x)-1$. 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 $y=-(\cot(x) - 1)=-\cot(x)+1$ (wrong). If we first reflect $y = \cot(x)$ about the $x$-axis to get $y=-\cot(x)$ and then translate 1 unit down we get $y=-\cot(x)-1$. If we translate first and then reflect we don't get the correct function. So the graph of $y = \cot(x)$ should be reflected about the $x$-axis before it is translated 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.