## IGCSE Mathematics 0580/04/SP/20 Q3

**3 **f(*x*) = 20/x + *x*, *x *≠ 0

**(a) **Complete the table.

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

**(c) **Using your graph, solve the equation f(*x*) = 11.

**(d) ***k *is a prime number and f(*x*) = *k *has no solutions. Find the possible values of *k*.

**(e) **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.

**(f) (i) **The equation f(*x*) = *x*2 can be written as *x*3 + *px*2 + *q *= 0.

Show that *p *= −1 and *q *= −20.

**(ii) **On the grid opposite, draw the graph of *y *= *x*2 for –4 ⩽ *x *⩽ 4.

**(iii) **Using your graphs, solve the equation *x*3 – *x*2 – 20 = 0.

**(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*.

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