Mathematics 0580 · IGCSE · Sketching curves

Sketching curves — practice question

Consider $f(x) = \frac{8}{x^2} + \frac{x}{2},\; x \neq 0.$
(a)[3]

Fill in the table of values for $f(x)$.

(b)[5]

On the grid, sketch the graph of $y=f(x)$ for $-5 \le x \le -1.5$ and $1.5 \le x \le 5$.

(c)[1]

Solve the equation $f(x)=0$.

(d)[3]

Using a suitable line drawn on the grid, solve $f(x)=1-x$.

(e)[3]

By drawing a tangent at the point $(-3, -0.6)$, estimate the gradient of the graph of $y=f(x)$ at $x=-3$.

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