1.1. $f(x)=\frac{20}{x}+x,x\neq0$

Complete the table.

1.2. On the grid, draw the graph of  $y=f(x)$ for $–10⩽x⩽–1.6$ and  $1.6⩽x⩽10$.

1.3. Using your graph, solve the equation $f(x)=11$.

$x$ = ..................   or   $x$ = .................

1.4. $k$ is a prime number and $f(x)=k$has no solutions.

Find the possible values of $k$.

1.5. The gradient of the graph of $y=f(x)$ at the point$(2,12)$is $−4$.

Write down the coordinates of the other point on the graph of $y=f(x)$ where the gradient is $−4$.

 (....................... , .......................)

1.6. i) The equation $f(x)={x}^{2}$ can be written as ${x}^{3}+p{x}^{2}+q=0.$

Show that $p=−1$and $q=−20$.

[2]

ii) On the grid, draw the graph of  $y={x}^{2}$ for  $–4⩽x⩽4$.   

[2]

iii) Using your graphs, solve the equation ${x}^{3}–{x}^{2}–20=0.$

$x$ = .............................................. [1]

iv)

The diagram shows a sketch of the graph of $y={x}^{3}–{x}^{2}–20.$ $P$ is the point $(n,0)$.

Write down the value of $n$.

$n=$ .............................................. [1]