Pretest

Question 1

Eve’s teacher asked her to graph the function y is equal to negative cotangent times x minus 1 by reflecting the graph of the function y is equal to cotangent of x about the x -axis and translating it vertically. Does it matter in which order Eve does the transformations?

Revolt · Accepted Answer

Yes, it matters. The graph of the function y is equal to cotangent of x should be reflected about the x -axis before it is translated 1 unit down.

Question 2

Where does the graph of the function y is equal to tangent of x have asymptotes?

Revolt · Accepted Answer

at the values of x where cosine of x is equal to 0

Question 3

What is the period of the function y is equal to tangent of open paren pi over 4 times open paren x minus pi over 3 close paren close paren ?

Revolt · Accepted Answer

3 units; 8 units

Question 4

The graph of the function y is equal to tangent of x was horizontally stretched so that its period became 10 pi Which is the equation of the transformed function?

Revolt · Accepted Answer

y is equal to tangent of open paren x over 5 close paren

Question 5

Suppose the graph of the parent function y is equal to cotangent of x is vertically compressed to produce the graph of the function y is equal to A cotangent x , but there are no reflections. Which describes the value of A ?

Revolt · Accepted Answer

0 is less than A comma A is less than 1

Question 6

Which is the graph of the function y is equal to negative tangent times x ?

Revolt · Accepted Answer

Image with description On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi by 2 units and the y axis ranges from negative 6 to 6 with an interval of 2 units. It shows a curve that oscillates between positive and negative infinity as x approaches multiples of pi. The curve has vertical asymptotes at x equals plus or minus n times pi by 2. The graph decreases in every pi interval as x decreases.The curve crosses the x axis at (2 pi comma 0), (pi comma 0) and (negative pi comma 0) and (negative 2 pi comma 0).

Question 7

Which is an asymptote of the graph of the function y is equal to tangent of open paren 3 fourths x close paren ?

Revolt · Accepted Answer

x is equal to negative 2 pi over 3

Question 8

Which is an asymptote of the graph of the function y is equal to cotangent of open paren x minus 2 pi over 3 close paren ?

Revolt · Accepted Answer

x is equal to negative 2 pi over 3; x is equal to 4 pi over 3

Question 9

What is the range of the function y is equal to cotangent of x ?

Revolt · Accepted Answer

all real numbers except pi over 2 plus n pi , where n is any integer

Question 10

Which function is equivalent to y is equal to negative cotangent times x ?

Revolt · Accepted Answer

y is equal to negative tangent times open paren x plus pi over 2 close paren

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