9.01 Transformations of 1/x
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.
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 equation $f\left(x\right)=\frac{4}{x}$f(x)=4x.
This graph shows the relationship between the current (in amperes) and resistance (in ohms) in an electrical circuit, when the voltage provided to the circuit is $240$240 V. The equation could be described as $\frac{240}{\text{Resistance}}=\text{Current}$240Resistance=Current
Boyle's law describes the relationship between pressure and volume of a gas of fixed mass under constant temperature. The pressure for a particular gas can be found using $P=\frac{6000}{V}$P=6000V, where $P$P has units kg/cm2 and $V$V has units cm3.