Question

determine the y-intercept and the equation for the horizontal asymptote of the function.
k(x)= (1/2)^x
Reminder: you might like to graph the function to help you.

a. (0.5, 1) there is no horizontal asymptote
b. (0,1); y= 0
c. (0, 0.5); y=0.5
d. (1,0); y= 1

Answer 1

k(x) = (1/2)ˣ
Since a (=1/2) is < 1, this exponential function is decreasing .
 y-intercept for x = 0
 k(x) =(1/2)⁰  → k(x) =1, then y-intercept = 1

Horizontal Asymptote:

lim k(x) = (1/2)ˣ = 0
x→∞

Horizontal asymptote x = 0