Hong Kong

Stage 4 - Stage 5

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

$4$4

A

$3$3

B

$2$2

C

$1$1

D

Easy

Approx 6 minutes

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

Ursula wants to sketch the graph of $y=\frac{7}{x}$`y`=7`x`, but knows that it will look similar to many other hyperbolas.

What can she do to the graph to show that it is the hyperbola $y=\frac{7}{x}$`y`=7`x`, rather than any other hyperbola of the form $y=\frac{k}{x}$`y`=`k``x`?

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

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