2016 TYS

The curve $y={{x}^{4}}$ is transformed onto the curves with equation $y=\text{f}\left( x \right)$. The turning point on $y={{x}^{4}}$ corresponds to the point with coordinates $\left( a,b \right)$ on $y=\text{f}\left( x \right)$. The curve $y=\text{f}\left( x \right)$ also passes through the point with coordinate $\left( 0,c \right)$. Given that $\text{f}\left( x \right)$ has the form $k{{\left( x-l \right)}^{4}}+m$ and that $a$, $b$ and $c$ are positive constants with $c>b$, express $k$, $l$ and $m$ in terms of $a$, $b$ and $c$.

[2]

By sketching the curve $y=\text{f}\left( x \right)$, or otherwise, sketch the curve $y=\frac{1}{\text{f}\left( x \right)}$. State, in terms of $a$, $b$ and $c$, the coordinates of any points where $y=\frac{1}{\text{f}\left( x \right)}$ crosses the axes and of any turning points.

[4]