21.09 The hyperbola
Interactive practice questions
Consider the graph of $y=\frac{2}{x}$y=2x.
For positive values of $x$x, as $x$x increases $y$y approaches what value?
$0$0
$1$1
$-\infty$−∞
$\infty$∞
As $x$x takes small positive values approaching $0$0, what value does $y$y approach?
$\infty$∞
$0$0
$-\infty$−∞
$\pi$π
What are the values that $x$x and $y$y cannot take?
$x$x$=$=$\editable{}$
$y$y$=$=$\editable{}$
The graph is symmetrical across two lines of symmetry. State the equations of these two lines.
$y=\editable{},y=\editable{}$y=,y=
Consider the graph of the function $y=\frac{4}{x}$y=4x.
$x=0$x=0 and $y=0$y=0 are lines that the curve approaches very closely as $x$x gets very small and very large.
What is the name of such lines?
Consider the function $y=\frac{2}{x}$y=2x.
Consider the function $y=-\frac{5}{x}$y=−5x.