Question

how do i find the intercept and horizontal asymptote of f(x)=2^x?

Answer 1

well, it's a basic property of exponential functions that they are bounded on the bottom by some value. The exponent can't be zero, but it can get very very close, (if you plugged in a big negative number, you'd get a number close to zero). That's you're horizontal asymptote. The function intercepts when x = 0, and another property of these functions, whenever you raise a number to an exponent, you get 1. Always.

Intercept: 1
asymptote: y = 0.

Answer 2

to find the (y) intercept, replace x with 0, as that will be the first coordinate for any y-intercept.

In this case, 2^(0)=1, so, the intercept is (0,1)

And as for the asymptote, this is a special case, as it's an exponential function. If you imagine any exponential function, they can always get CLOSE to 0, but never actually there. This is the exact definition of an asymptote, and thus, IS the asymptote.

Asymptote: y=0