Given:#" "f(x)=0.72^x-2#
There are three prime conditions for this expression
Condition 1: #x>0#
Condition 2: #x<0#
Condition 3: #x=0#
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#color(blue)("Consider condition 3 ")x=0#
When #x=0" "f(x)# is defined as it has a definite value.
Thus #color(blue)(x=0 " is NOT an asymptote")#
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#color(blue)("Consider condition 2 ") x<0#
The #f(x)# takes the form #1/(0.72^x)-2#
When #x=0": "f(x)=1-2" "# thus defined
As #x# becomes bigger #0.72^2# becomes smaller so
#1/(0.72^2)" "#becomes bigger
Thus #lim_(xtooo) f(x)->oo# (infinity is not a number!)
#color(brown)("Is this an asymptote? I have invited another mathematician to look at this bit!")#
Gut feeling is that this is NOT an asymptote!!!!!
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#color(blue)("Consider condition 1 ") x>0#
As #x# becomes increasingly larger #0.72^x# becomes increasingly smaller and smaller.
So# lim_(xtooo) 0.72^x-2 -> -2color#
#color(blue)(-2" Is an asymptote")#
