Which situations are modeled accurately by a periodic function? Select all that apply.

Here is the graph of a function for some values of \(x\).

1. Can you extend the graph to the whole plane so that the function \(f\) is periodic? Explain your reasoning.
2. Can you extend the graph to the whole plane so that the function \(f\) is not periodic? Explain your reasoning.

1. Can a non-constant linear function be periodic? Explain your reasoning.
2. Can a quadratic function be periodic? Explain your reasoning. 

Do \((7,1)\) and \((\text-5,5)\) lie on the same circle centered at \((0,0)\)? Explain how you know.

The measure of angle \(\theta\) is between 0 and \(2\pi\) radians. Which statements must be true of \(\sin(\theta)\) and \(\cos(\theta)\)? Select all that apply.

The center of a clock is the origin \((0,0)\) in a coordinate system. The hour hand is 4 units long. What are the coordinates of the end of the hour hand at:

1. 3:00
2. 8:00
3. 11:00

A parabola is transformed from \(y=x^2\) to \(y=\text-\frac12x^2+6x-17\). 

1. Write an equation for the parabola in vertex form. 
2. What transformations were applied to the parabola?