The function \( y = 2\left(\frac{6}{5}\right)^x \) is a continuous function.
Exponential functions, generally of the form \( y = a \cdot b^x \), where \( a \) is a constant and \( b \) is a positive real number, are continuous for all real values of \( x \). Since the exponential function does not take on only isolated points but instead covers an entire range of values continuously as \( x \) varies, it is classified as continuous.
Therefore, the correct answer is Continuous.