New Zealand
Level 7 - NCEA Level 2

# Graphing 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.

c

Hence draw the curve.

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

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

Ursula wants to sketch the graph of $y=\frac{7}{x}$y=7x, 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=7x, rather than any other hyperbola of the form $y=\frac{k}{x}$y=kx?

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

### Outcomes

#### M7-2

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

#### 91257

Apply graphical methods in solving problems