Question

What is the asymptote of the graph of the function f(x)=-6^x+4

Answer 1

The asymptote occurs on one end of the exponential function, where you get larger negative exponents.
Notice that:
\( 6^x \)
For a negative number, say x = -a, a>0
\( 6^{-a} = \dfrac{1}{6^a} \)
For larger and larger negative values (large positive a), the denominator gets very very big, and numerator is a measly 1. 1/ huge numbers tends towards a tiny value, near 0. So the end behavior of the function is that 6^x --> 0, and y = -6^x + 4 = 0 + 4