Given: \(f(x)=\frac{4}{x}+2 \quad\) and \[ x^{2}+y^{2}=9 \] Write down the equations of the asymptotes of \(f(x)\).

Question

Given: \(f(x)=\frac{4}{x}+2 \quad\) and
\[
x^{2}+y^{2}=9
\]
1. Write down the equations of the asymptotes of \(f(x)\).
2. Determine the coordinates of the \(x\) - and \(y\)-intercepts of \(f(x)\).
3. Determine the radius of the circle.
4. Sketch the circle and the graph of \(f(x)\) on the same system, indicating all the asymptotes and the intercepts with the axes.
5. Determine the equation of the line of symmetry of \(f(x)\), with a negative gradient.
6. What is the range of \(f(x)\) ?
7. Give the domain of the circle.