NZ Level 7 (NZC) Level 2 (NCEA)

Graphing Hyperbolas

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

$4$4

A

$3$3

B

$2$2

C

$1$1

D

Easy

Approx 6 minutes

Sign up to try all questions

Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs

Apply graphical methods in solving problems