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In this lesson, we will learn how to graph the tangent function and the arctangent function and describe the features of these graphs.

Q1:

Find the exact value of t a n t a n − 1 − 5 𝜋 6 in radians.

Q2:

Which of these two value tables shows a domain of the tangent function that can be used to construct its inverse function?

Table A

Table B

Q3:

Which of the following is the graph of 𝑦 = 𝑥 t a n ?

Q4:

Which of the following is the graph of 𝑦 = ( 𝑥 + 9 0 ) t a n ?

Q5:

What is the domain of the function t a n − 𝜋 𝑥 2 whose graph is shown?

Q6:

Find the exact value of t a n − 1 ( − 1 ) in radians in the interval − 𝜋 < 𝜃 ≤ 2 𝜋 3 .

Q7:

Which of the following is the graph of 𝑦 = − ( 𝑥 ) t a n ?