Consider the function $y=\frac{1}{x}$y=1x which is defined for all real values of $x$x except $0$0.
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 | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
Plot the points in the table of values.
Hence draw the curve.
In which quadrants does the graph lie?
$4$4
$3$3
$2$2
$1$1
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