Asymptote equation

Question

What is the asymptote equation for each one of the graphs?

a) f(x) = 2(3)^x + 1 c) h(x) = -5(1.5)^x

b) g(x) = -1/2(1/3)^x d) b(x) = 4(1/2)^x

Answer 1

I'll assume you are talking about horizontal asymptotes. Any exponential function of the form f(x) = a·b^x + c (where b ≠ 1) has a horizontal asymptote of y = c. If you don't see a "c" being added or subtracted, the asymptote is y = 0.

Examples:

f(x) = 7·2^x + 4 has an asymptote of y = 4

g(x) = 0.6·10^x - 15 has an asymptote of y = -15

h(x) = 3·(-0.2)^x has an asymptote of y = 0 since there is nothing being added or subtracted from the function.

I hope that helps out.