Graphing Tangent and Cotangent Quiz

Suppose the graph of the parent function y=cot(x) is vertically compressed to produce the graph of the function y=a cot(x), but there are no reflections. Which describes the value of a?

0 is greater than a which is greater than 1

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

4 units

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

Which is the graph of the function y= -tan(x)?

B

What are the x-ints 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 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 appplied 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

What function is graphed below?

D y=tan(x) +2

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

D y=tan(x+pi/2)

What function is graphed below?

NOT C y=cot(3/4(x+ pi/6)

The graph of the function y=tan(x) was horizontally stretched so that its period became 10pi. What is the equation of the transformed function?

NOT y= tan(10x)

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

at the values of x where cos(x)=0

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

x= -2pi/3