Mathematics 0580 · IGCSE · Graphs of functions

Graphs of functions — practice question

The function is given by $f(x)=\frac{20}{x}+x$, $x\neq 0$.
(a)[2]

Complete the table.

(b)[5]

On the grid, draw the graph of $y=f(x)$ for $-10\le x\le -1.6$ and $1.6\le x\le 10$.

(c)[2]

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

(d)[2]

Find the possible values of $k$.

(e)[1]

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

(f(i))[2]

Show that $p=-1$ and $q=-20$.

(f(ii))[2]

Using the grid opposite, sketch the graph of $y=x^2$ for $-4\le x\le 4$.

(f(iii))[1]

From your graphs, solve the equation $x^3-x^2-20=0$.

(f(iv))[1]

Give the value of $n$.

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