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iGCSE (2021 Edition)

17.08 The Hyperbola

Interactive practice questions

Consider the graph of $y=\frac{2}{x}$y=2x.

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a

For positive values of $x$x, as $x$x increases $y$y approaches what value?

$0$0

A

$1$1

B

$-\infty$

C

$\infty$

D
b

As $x$x takes small positive values approaching $0$0, what value does $y$y approach?

$\infty$

A

$0$0

B

$-\infty$

C

$\pi$π

D
c

What are the values that $x$x and $y$y cannot take?

$x$x$=$=$\editable{}$

$y$y$=$=$\editable{}$

d

The graph is symmetrical across two lines of symmetry. State the equations of these two lines.

$y=\editable{},y=\editable{}$y=,y=

Easy
2min

Consider the graph of the function $y=\frac{4}{x}$y=4x.

$x=0$x=0 and $y=0$y=0 are lines that the curve approaches very closely as $x$x gets very small and very large.

What is the name of such lines?

Easy
< 1min

Consider the function $y=\frac{2}{x}$y=2x.

Easy
3min

Consider the function $y=-\frac{5}{x}$y=5x.

Easy
2min
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Outcomes

0607C3.5

Understanding of the concept of asymptotes and graphical identification of simple examples parallel to the axes.

0607E3.5

Understanding of the concept of asymptotes and graphical identification of simple examples parallel to the axes.

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