GCSE · Graphs of functions

Cubic, reciprocal and exponential graphsExam-style questions

The shape vocabulary of the Higher course — S-curve cubics, two-branch reciprocals with asymptotes, ever-positive exponentials — and why each equation forces its shape.

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15 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 3 Level 4 Level 5

1
The curve $y = x^3 - 4x$ crosses the $x$ -axis at three points.

Find the $x$ -coordinate of each of the three points.
Level 5 · 3 marksTry it
2
A curve has ALL three of these properties:
- it passes through $(0, 1)$
- $y$ is positive for every value of $x$
- as $x$ becomes more negative, $y$ gets closer and closer to $0$
Which of the following could be its equation? Explain why each of the others is impossible.

$y = x^2 + 1 \qquad y = 2^x \qquad y = \dfrac{1}{x} \qquad y = x^3 + 1$
Level 5 · 3 marksTry it