Exam-Style Question on Graphs

Question id: 711. This question is similar to one that appeared on a GCSE Higher paper in 2022. The use of a calculator is allowed.

(a) Sketch the graph of $ y = f(x) $ for values of $ x $ between $-5$ and $5$ given that:

$$ f(x) = \frac{1}{x-1} - x $$

(b) Write down the equations of any asymptotes parallel to the $ y $-axis.

(d) Find the coordinates of the x-axis intercepts.

(e) Find a value of $ k $ for which $ g(x) = kx $ does not intercept $ f(x)$.

(f) Draw the graph of $h(x)=x-3$ on the same set of axes.

(g) Solve the equation $ f(x) = h(x) $.

(h) Find the solutions to the inequality $ f(x) > h(x) $.

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Exam-Style Question on Graphs

A mathematics exam-style question with a worked solution that can be revealed gradually

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