How do you graph (-5x)/(x+3)?

1 Answer
Alan P.
Aug 30, 2015

Establish the asymptotes and a few data points; then sketch the graph based on this information.

Explanation:

Note that f(x)=(-5x)/(x+3) is undefined for x=-3
and
color(white)("XXXX")f(x) rarr +oo as (x+3) rarr -0
color(white)("XXXX")f(x) rarr -oo as (x+3) rarr +0

Therefore x=-3 is an asymptote
with f(x) positive if x< -3
and f(x) negative if x > -3

Furthermore,
(-5x)/(x+3) = -5 + 15/(x+3)

as abs(x) rarr oo, 15/(x+3) rarr 0

therefore f(x) = -5 is an asymptotic value.

Combining this information with a few data points:
color(white)("XXX") {: (x," ",f(x)), (-2," ",10), (0," ",0), (2," ",-2), (-4," ",-20), (-6," ",-10), (-8," ",-8) :}
and drawing the graph should not be difficult.
graph{(-5x)/(x+3) [-30.68, 34.26, -20.04, 12.45]}

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