GCSE · Graphs of functions

Cubic and reciprocal graphs (tables, plotting and asymptotes)Exam-style questions

Draw y = x³ − 3x and y = 4/x from a table of values (a cube keeps its sign, and there is no point at x = 0), join the points with one smooth curve (two separate branches for a reciprocal), read the solutions of an equation off the curve, and know the shapes of ±x³ and ±k/x and the asymptotes they never touch.

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

DifficultyAll Level 2 Level 3 Level 4

1
Here is an incomplete table of values for $y = \dfrac{6}{x}$
$x$ $-6$ $-3$ $-2$ $-1$ $1$ $2$ $3$ $6$
$y$ $-1$ $-3$ $6$ $2$ $1$
(a) Complete the table.

(2 marks)
(b) Explain why the table has no value of $y$ for $x = 0$

(1 mark)
Level 2 · 3 marksTry it
2
The graph of $y = x^3 - 4x + 1$ is drawn on the grid.Use the graph to find estimates for the solutions of $x^3 - 4x + 1 = 0$

(2 marks)
Level 2 · 2 marksTry it
3
$y = \dfrac{20}{x}$
(a) Work out the value of $y$ when $x = 1000$

(1 mark)

Jay says,

"When $x$ is big enough, $y$ will be $0$ "
(b) Is Jay correct?

You must give a reason for your answer.

(1 mark)
Level 2 · 2 marksTry it
4
Lena draws the graph of $y = \dfrac{6}{x}$ for values of $x$ from $-6$ to $6$

Here is her graph.What mistake has Lena made?

(1 mark)
Level 2 · 1 markTry it
5
(a) Complete the table of values for $y = x^3 - 2x + 1$
$x$ $-2$ $-1$ $0$ $1$ $2$
$y$ $-3$ $1$
(2 marks)
(b) On the grid, draw the graph of $y = x^3 - 2x + 1$ for values of $x$ from $-2$ to $2$ (2 marks)
(c) Use your graph to find estimates for the solutions of the equation

$x^3 - 2x + 1 = 2$

(2 marks)
Level 3 · 6 marksTry it

$x$	$-6$	$-3$	$-2$	$-1$	$1$	$2$	$3$	$6$
$y$	$-1$		$-3$		$6$		$2$	$1$

$x$	$-2$	$-1$	$0$	$1$	$2$
$y$	$-3$		$1$

11 more questions on cubic and reciprocal graphs (tables, plotting and asymptotes)

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