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5.10 Hyperbolas

Interactive practice questions

Consider the function $y=\frac{1}{x}$y=1x which is defined for all real values of $x$x except $0$0.

a

Complete the following table of values.

$x$x $-2$2 $-1$1 $-\frac{1}{2}$12 $-\frac{1}{4}$14 $\frac{1}{4}$14 $\frac{1}{2}$12 $1$1 $2$2
$y$y $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
b

Plot the points in the table of values.

Loading Graph...
c

Hence draw the curve.

Loading Graph...
d

In which quadrants does the graph lie?

$3$3

A

$2$2

B

$1$1

C

$4$4

D
Easy
5min

Consider the function $y=\frac{3}{x}$y=3x

Easy
2min

Consider the function $y=-\frac{1}{x}$y=1x

Easy
3min

Consider the function $y=-\frac{1}{2x}$y=12x

Easy
2min
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Outcomes

VCMNA359 (10a)

Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations.

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