f(x)=4^x + 1 state the domain, range, intercepts, and asymptotes

Answer 1

this is an exponential function with similar properties as e^x only f(x) here has base 2 instead of e, and it's been shifted up by 1, to get a y intercept of 2.

any number raised to 0 power = 1. f(0) = 4^0 + 1 = 1+1 = 2, when x =0 then f(0) = the y intercept

domain = any real number, (-infinity,infinity)

range = any positive real number (0,infinity)

only one intercept, the y intercept = 2. there is no x intercept

only one asymptote: the x axis, y=0