State Asymptote Equation for f(x)=5^(-x) + 4

Question

Y Intercept ordered pair is (0,5)

Answer 1

As x gets "large", the first term in the expression approaches 0.  Remember that 5^-x = 1/5^x 

 

Therefore f(x) approaches 4.  So as x gets large the the function approaches the line f(x) = 4 (asymptote).

 

If you check what happens x becomes a large but -ve number, the function grows positively without bound.  So there is no asymptote in that direction. 

 

as a side note 

Also the domain of x is all real numbers, and the range of the function is f(x) > 4.  . but approaches 4 as x gets large in a positive direction