21.09 The hyperbola
Interactive practice questions
Consider the graph of $y=\frac{2}{x}$y=2x.
A Cartesian plane has an $x$x-axis and $y$y-axis ranging from $-10$−10 to $10$10. Each axis has major tick marks at $2$2-unit intervals and minor tick marks at $1$1-unit intervals. A graph of the hyperbola $y=\frac{2}{x}$y=2x is plotted with two symmetrical branches. One branch lies in the first quadrant curving downward and rightward. And the other branch lies in the third quadrant curving downward and leftward.
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.