Hyperbolas and Other Rational Functions
India
Class XI
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
Easy
5min
Consider the function $y=\frac{2}{x}$y=2x
Easy
2min
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?
Easy
< 1min
Consider the function $y=-\frac{1}{x}$y=−1x
Easy
3min
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