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.

Question

Hugo Ward

Mathematics

31 January, 11:51

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.

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Answers (1)

Know the Answer?

Carl Kaiser · Answer 1

cot (x) is called cotangent function and it is defined with the radio cos (x) / sin (x). The cotangent function has values from negative infinity to positive infinity,

This is the reason why adding to or subtracting from the cotangent function doesn’t change what values it has.

Reflecting the graph of the cotangent function about the x-axis will result in the tangent function. Translating this function will not make any changes.

So, it doesn’t matter in which order Eve will do the transformation: C and D (they are the same)