Sketch absolute value of function

7. $$f ( x ) = x ^ { 4 } - 4 x - 8$$

1. Show that there is a root of \(\mathrm { f } ( x ) = 0\) in the interval \([ - 2 , - 1 ]\).
2. Find the coordinates of the turning point on the graph of \(y = \mathrm { f } ( x )\).
3. Given that \(\mathrm { f } ( x ) = ( x - 2 ) \left( x ^ { 3 } + a x ^ { 2 } + b x + c \right)\), find the values of the constants, \(a , b\) and \(c\).
4. In the space provided on page 21, sketch the graph of \(y = \mathrm { f } ( x )\).
5. Hence sketch the graph of \(y = | \mathrm { f } ( x ) |\).

9. \includegraphics[max width=\textwidth, alt={}, center]{5e6a37a1-c51f-4637-aaae-48da6ab3eca0-3_727_1022_244_342} The diagram shows the curve with equation \(y = \mathrm { f } ( x )\). The curve crosses the axes at \(( p , 0 )\) and \(( 0 , q )\) and the lines \(x = 1\) and \(y = 2\) are asymptotes of the curve.

1. Showing the coordinates of any points of intersection with the axes and the equations of any asymptotes, sketch on separate diagrams the graphs of
   1. \(y = | \mathrm { f } ( x ) |\),
   2. \(y = 2 \mathrm { f } ( x + 1 )\). Given also that $$\mathrm { f } ( x ) \equiv \frac { 2 x - 1 } { x - 1 } , \quad x \in \mathbb { R } , \quad x \neq 1$$
2. find the values of \(p\) and \(q\),
3. find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).