Question 939777
Given the curve {{{y=3(1/2)^x-1}}} or {{{y=3/2^x-1}}}
Determine,

a) 

the horizontal asymptote is x-axis

{{{lim(x->infinity, (3/2^x)-1 =-1 )}}}

{{{y = 3/2^x-1}}} is asymptotic to {{{y = -1}}}

b)
the y-intercept

{{{y=3/2^x-1}}} if {{{x=0}}}=> {{{y=3/2^0-1}}}=> {{{y=3/1-1}}}=> {{{y=2}}}

the y-intercept at ({{{0}}},{{{2}}})


c) 
the domain : {{{R}}} all real numbers


the range:{ {{{y}}} element {{{R}}} : {{{y>-1}}} }  (all positive real numbers)


d)

if its always increasing or decreasing

it is always {{{decreasing}}} because the y-value decreases as the x-value increases


{{{ graph( 600, 600, -25,25, -10, 10,-1,-1, 3/2^x-1,3/2^x-1) }}}