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 some graphs.Write the letter of the matching graph next to each equation in the table.
Equation Letter of graph
$y = 2x - 1$
$y = -\dfrac{3}{x}$
$y = 0.5^x$
$y = x^3 - 4x$
(3 marks)
Level 4 · 3 marksTry it
2
The sketch shows part of the curve with equation $y = k^x$ , where $k$ is a positive constant.The point $P(-2, 0.36)$ is on the curve.

Find the value of $k$ .

(2 marks)
Level 4 · 2 marksTry it
3
(a) Write down the coordinates of the point where the graph of $y = 2^x$ crosses the $y$ -axis.

(b) Explain why the graph of $y = 2^x$ never touches the $x$ -axis.
Level 4 · 2 marksTry it
4
(a) Explain why the graph of $y = \dfrac{1}{x}$ has no point where $x = 0$

(b) Write down the coordinates of the point on the graph of $y = \dfrac{1}{x}$ where $x = \dfrac{1}{2}$
Level 4 · 2 marksTry it
5
$y = 3^x$

(a) Work out the value of $y$ when $x = 4$

(b) Work out the value of $x$ when $y = \dfrac{1}{3}$
Level 4 · 2 marksTry it

Equation	Letter of graph
$y = 2x - 1$
$y = -\dfrac{3}{x}$
$y = 0.5^x$
$y = x^3 - 4x$

2 more questions on cubic, reciprocal and exponential graphs

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