Mathematics 0580 · IGCSE · Graphs of functions

Graphs of functions — practice question

The function has rule $f(x) = x^2 - \frac{1}{x} - 4$, $x \ne 0$.
(a(i))[2]

Fill in the table.

(a(ii))[5]

On the grid, plot the graph of $y = f(x)$ for $-3 \le x \le -0.1$ and $0.2 \le x \le 3$.

(b)[3]

Use your graph to determine the solutions of $f(x) = 0$.

(c)[1]

Give an integer $k$ such that $f(x) = k$ has exactly one solution.

(d(i))[4]

Draw an appropriate straight line to solve $f(x) + 2 = -5x$.

(d(ii))[2]

The equation $f(x) + 2 = -5x$ may be expressed as $x^3 + ax^2 + bx - 1 = 0$. Determine the value of $a$ and the value of $b$.

Worked solution & mark scheme

This 17-mark question has a full step-by-step worked solution and mark scheme. One marking point: Hence $x=-2$.

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