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
Which of these equations has a straight-line graph? $\quad$ A: $y = x^2 \qquad$ B: $y = 3x - 1 \qquad$ C: $y = \dfrac{1}{x}$
Level 1 · 1 markTry it
2
Here is a sketch of a graph.Which of these could be its equation? $\quad$ A: $y = x^2 \qquad$ B: $y = x^3 \qquad$ C: $y = 2x$
Level 1 · 1 markTry it
3
Here is a sketch of a graph.Which of these could be its equation? $\quad$ A: $y = x^2 \qquad$ B: $y = \dfrac{1}{x} \qquad$ C: $y = x + 1$
Level 1 · 1 markTry it
4
Here are four graphs, A, B, C and D.(a) Write down the letter of the graph of $y = x^3$

(b) Write down the letter of the graph of $y = \dfrac{1}{x}$
Level 3 · 2 marksTry it
5
Here are four graphs, A, B, C and D.Write down the letter of the graph that could be

(a) $y = -x^2$

(b) $y = \left(\dfrac{1}{2}\right)^x$

(c) $y = x^3 - 3x$
Level 3 · 3 marksTry it

10 more questions on cubic, reciprocal and exponential graphs

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