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
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
2
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
3
$y = \dfrac{6}{x}$ for $x \neq 0$

(a) Work out the value of $y$ when: $\;x = 1$ , $\;x = 2$ , $\;x = 3$

(b) Explain why the graph of $y = \dfrac{6}{x}$ never crosses the $y$ -axis.
Level 3 · 3 marksTry it