How do you graph $\frac{2 x}{x - 4}$ $(2x)/(x-4)$ ?

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How do you graph $\frac{2 x}{x - 4}$ $(2x)/(x-4)$ ?

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Answer 1 · 2015-07-31T01:32:56

Graph as $y = \frac{2 x}{x - 4}$ $y = (2x)/(x-4)$
by establishing a few data points with random values of $x$ $x$ and noting the asymptotic limits at $y = 2$ $y=2$ and $x = 4$ $x=4$

Explanation:

The asymptotic limit $x = 4$ $x=4$ should be obvious from the expression (since division by 0 is undefined).

$y = \frac{2 x}{x - 4}$ $y=(2x)/(x-4)$ is equivalent to $y = \frac{2}{1 - \frac{4}{x}}$ $y=2/(1-4/x)$ [provided we ignore the special case $x = 0$ $x=0$ ]
As $x \to \pm \infty$ $x rarr +-oo$
$XXXX$ $color(white)("XXXX")$ $\frac{4}{x} \to 0$ $4/x rarr 0$
and
$XXXX$ $color(white)("XXXX")$ $y = \frac{2}{1 - \frac{4}{x}} \to \frac{2}{1} = 2$ $y=2/(1-4/x) rarr 2/1 = 2$
giving the horizontal asymptotic limit.

A few test values for $x$ $x$ , such as
$XXXX$ $color(white)("XXXX")$ $x = 0 \to y = 0$ $x=0 rarr y=0$
$XXXX$ $color(white)("XXXX")$ $x = 2 \to y = - 2$ $x=2 rarr y = -2$
$XXXX$ $color(white)("XXXX")$ $x = 5 \to y = 10$ $x=5 rarr y=10$
$XXXX$ $color(white)("XXXX")$ $x = - 4 \to y = - 1$ $x=-4 rarr y = -1$
help give shape to the graph

graph{(2x)/(x-4) [-25.3, 26, -11.27, 14.4]}

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How do you graph $\frac{2 x}{x - 4}$ $(2x)/(x-4)$ ?

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