How do you graph #y=5(3^x)+1#? What is the #y#-intercept and the domain and range?

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Answer 1 · 2018-07-15T07:39:02

Please see the explanation below.

The function is

#y=5*3^x+1#

The graph is as follows

graph{5*3^x+1 [-12.82, 15.65, -3.3, 10.94]}

The y-intercept is when #x=0#

That is

#y=5*3^0+1=5*1+1=6#

The y-intercept is the point #=(0,6)#

For this function, the domain is #x in RR#

#lim_(x->-oo)y=lim_(x->-oo)5*3^x+1#

#=5*3^(-oo)+1#

#=5*0+1=1#

#lim_(x->+oo)y=lim_(x->+oo)5*3^x+1#

#=5*3^(+oo)+1#

#=+oo#

Therefore,

The range is #y in (1, +oo)#