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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