Find the equation of the horizontal asymptote of the given equation

Question

f(x)=5^(x-2)+3

Answer 1

The graph of y = 5^x lies above the x-axis and approaches the x-axis as x→ -∞.

So, y = 0 (the x-axis) is the horizontal asymptote for y = 5^x.

The graph of y = 5^(x-2) +3 is obtained from the graph of y = 5^x by translating the graph of y = 5^x two units to the left and three units upward.

So, the horizontal asymptote is y = 3.