Graphing Tangent and Cotangent Quiz

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.

Where does the graph of the function y = tan(x) have asymptotes?

[A] at the values of x where cos(x) = 0

What is the period of the function y = tan(pi/4(x - pi/3))?

[B] 4 units

Which is an asymptote of the graph of the function y= tan(3/4x) ?

[B] x = -2pi/3

Which is an asymptote of the graph of the function y = cot(x - 2pi/3)?

[B] x = -pi/3

What are the x-intercepts of the graph of the function y = 6tan(x/2) - 3 ? Use your graphing calculator to estimate the answer.

[C] (0.9273 + 2npi , 0) where n is any integer

Chris wanted to transform the graph of the parent function y = cot(x) by horizontally compressing it so that it has a period of pi/2 units, horizontally translating it pi/4 units to the right, and vertically translating it 1 unit up. To do so, he graphed the function y = cot(2x - pi/4) + 1, as shown. What did he do wrong?

[C] He graphed the function y = cot(2x - pi/4) + 1 correctly, but it was not the right function to graph. He should have graphed y = cot(2x - pi/2) + 1.

What function is graphed below?

[C] y = cot(x + pi/4)

What transformations were applied to the graph of the parent function y = tan(x) to produce the function graphed below?

[D] a horizontal stretch to produce a period of 3pi/2 and a horizontal translation of pi/4 units to the right

Which function is equivalent to y = -cot(x)?

[D] y = tan(x + pi/2)