Mathematics 0580 · IGCSE · Sketching curves

Sketching curves — practice question

The function is given by $f(x)=x-\frac{1}{2x^2}$, $x\neq0$.
(a)[2]

Fill in the table of values.

(b)[5]

On the grid, sketch $y=f(x)$ for $-3\le x\le-0.3$ and $0.3\le x\le2$.

(c)[1]

Solve $f(x)=1$ using your graph.

(d)[1]

There is exactly one negative integer value, $k$, for which $f(x)=k$ has only one solution for all real $x$. State this value of $k$.

(e(i))[1]

Determine the equation of this straight line.

(e(ii))[3]

On the grid, draw this straight line and use it to solve $2x-\frac{1}{2x^2}-2=0$.

Worked solution & mark scheme

This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: The value $x=-1.5$ is correct.

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