SOLUTION: Given the curve y=3(1/2)^x Determine, a) the horizontal asymptote b)the y-intercept c) the domain and range d)if its always increasing or decreasing

Algebra ->  Exponents -> SOLUTION: Given the curve y=3(1/2)^x Determine, a) the horizontal asymptote b)the y-intercept c) the domain and range d)if its always increasing or decreasing      Log On


   

Question 939777: Given the curve y=3(1/2)^x
Determine,
a) the horizontal asymptote
b)the y-intercept
c) the domain and range
d)if its always increasing or decreasing
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Given the curve y=3%281%2F2%29%5Ex-1 or y=3%2F2%5Ex-1
Determine,
a)
the horizontal asymptote is x-axis
lim%28x-%3Einfinity%2C+%283%2F2%5Ex%29-1+=-1+%29
y+=+3%2F2%5Ex-1 is asymptotic to y+=+-1
b)
the y-intercept
y=3%2F2%5Ex-1 if x=0=> y=3%2F2%5E0-1=> y=3%2F1-1=> y=2
the y-intercept at (0,2)

c)
the domain : R all real numbers

the range:{ y element R : y%3E-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%28+600%2C+600%2C+-25%2C25%2C+-10%2C+10%2C-1%2C-1%2C+3%2F2%5Ex-1%2C3%2F2%5Ex-1%29+