Question

Graph the function below. Determine the domain, range, and horizontal asymptote. Please show all of your work.
f(x) = 3 - (1/2)^x

Answer 1

ok we go slow
domain: all real numbers since you can raise 1/2 to any power you like

Answer 2

range: no matter what x is
\[(\frac{1}{2})^x>0\] and so
\[3-(\frac{1}{2})^x<3\] and your range is
\[(-\infty, 3)\]

Answer 3

since that is your range, you know horizontal asymptote is
\[y=3\] and here is a decent picture

Answer 4

i dont see the picture. lol

Answer 5

so what would the domain be?