(a)[2]
State the range of $f$.
(b)[2]
A function $g$ is defined by $g(x) = f(x) + k$, where $k$ is a positive constant. The $x$-axis is a tangent to the curve $y = g(x)$. State the value of $k$ and hence describe fully the transformation that maps the curve $y = f(x)$ on to $y = g(x)$.
(c)[1]
State the equation of the curve that is the reflection of $y = f(x)$ in the $x$-axis. Give your answer in the form $y = a\cos 2x + b$, where $a$ and $b$ are constants.