NZ Level 7 (NZC) Level 2 (NCEA)
topic badge
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.

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

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

What is Mathspace

About Mathspace