Question

Eve’s 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?
A.) 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.

B.) 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.

C.) No, it doesn’t 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.

D.) No, it doesn’t 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 1

Answer:

A on edge

Step-by-step explanation:

Answer 2

Answer:

The correct answer is A: Yes, it matters. The graph of a function y = cot(x) should be reflected about the x-axis before it is translated 1 unit up.

Step-by-step explanation:

The reason being is that when there are two factors that affect a graph's verticality, order does matter. Here is the exact reasoning:

Say you translated 1 unit down first. You would then have y = cot(x) - 1. Then, in order to reflect it about the x axis, you must multiply the entire right side of the equation by negative 1. So now you have y = -1(cot(x) -1), which, when distributed, gives you: y = -cot(x) + 1, instead of y = -cot(x) -1. Therefore, you must reflect before you translate.

And you may be wondering, why then, isn't D correct? Since, you could fix that by translating up 1 and then reflecting, so that you get the final product. Well, it specifies that it can be done in any order. So one way you could get the equation you want, but the other way, you get y = -cot(x) + 1, which, again, is incorrect.

I hope this cleared it up for you!