Lesson 12

Here is a graph of \(f\) given by \(f(\theta) = \tan(\theta)\).

1. Are \(\frac{\pi}{2}\) and \(\frac{3\pi}{2}\) in the domain of \(f\)? Explain how you know.
2. What are the \(\theta\)-intercepts of the graph of \(f\)? Explain how you know.

The function \(f\) is given by \(f(\theta) = \tan(\theta)\). Which of the statements are true? Select all that apply. 

\(f\) is a periodic function

The domain of \(f\) is all real numbers.

The range of \(f\) is all real numbers.

The period of \(f\) is \(2\pi\).

The period of \(f\) is \(\pi\).

For which angles \(\theta\) between 0 and \(2\pi\) is \(\cos(\theta) < 0\)? Explain how you know.

It is 3:00 a.m.

1. What angle will the hour hand rotate through in the next hour? Explain how you know. 
2. What angle will the hour hand rotate through in the next 12 hours? Explain how you know.
3. What angle will the hour hand rotate through in the next 24 hours? Explain how you know. 

The function \(f\) is given by \(f(x) = x^2\).

1. Write an equation for the function \(g\) whose graph is the graph of \(f\) translated 3 units left and then reflected over the \(y\)-axis.
2. Write an equation for the function \(h\) whose graph is the graph of \(f\) reflected over the \(y\)-axis and then translated 3 units to the left.
3. Do \(g\) and \(h\) have the same graph? Explain your reasoning.