How do you graph #y=(1/3)^x+1#?

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Answer 1 · 2017-12-29T21:41:24

See below.

First find common coordinates:

y axis intercept occurs when #x=0#:

#y=(1/3)^(0)+1=2color(white)(88)# coordinate #( 0 , 2 )#

x axis intercepts occur when #y=0#:

#(1/3)^x+1=0# ( no real number solutions to this )

No x axis intercepts.

as #x->oo# , #color(white)(88)(1/3)^x+1->1#

as #x->-oo# , #color(white)(88)(1/3)^x+1->oo#

The line #y=1# is a horizontal asymptote.

GRAPH:

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