6. (10 points) Suppose a sinusoidal function $f(x)$ is given, with the following values defined: $a_0$ is the minimum value of $f(x)$, $a_1$ is the maximum value of $f(x)$, and $b_0$, $b_1$ satisfy that $f$ is increasing on the interval $[b_0, b_1]$ and $f(b_0) = a_0$, $f(b_1) = a_1$. In the following parts, your answer should be in terms of some of $a_0$, $a_1$, $b_0$, $b_1$.
(a) (3 points) What is the amplitude of $f(x)$?
(b) (2 points) What is its average value?
(c) (3 points) What is the period of $f(x)$?
(d) (2 points) Give a formula for $f(x)$.
