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?\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: Analyze reflection about x - axis

When we reflect the graph of $y = \cot(x)$ about the $x$-axis, the transformation is $y=-\cot(x)$.

Step2: Analyze vertical translation

The function $y =-\cot(x)-1$ is obtained by translating the graph of $y =-\cot(x)$ 1 unit down. 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 $y=-(\cot(x)-1)=-\cot(x) + 1$, which is incorrect. 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 consider the general rules of function transformations, for a function $y = f(x)$, reflection about the $x$-axis gives $y=-f(x)$ and vertical translation $k$ units down gives $y=-f(x)-k$. Here $f(x)=\cot(x)$ and $k = 1$. The graph of the function $y=\cot(x)$ 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.