Given the exponential function y=2(

Question

6
5
​
)
x
, what is the horizontal asymptote?

y=8

y=1

y>0

y=0

Answer 1

The horizontal asymptote of an exponential function in the form \( y = a \cdot b^x \) occurs as \( x \) approaches negative infinity if \( a > 0 \) and \( 0 < b < 1 \).

For the given function \( y = 2\left(\frac{6}{5}\right)^x \):

1. Since \( \frac{6}{5} > 1 \), as \( x \) approaches negative infinity, \( \left(\frac{6}{5}\right)^x \) approaches \( 0 \).
2. Therefore, the function approaches:

\[ y = 2 \cdot 0 = 0 \]

This means the horizontal asymptote is \( y = 0 \).

The correct answer is:

y = 0.