Is this an exponential distribution?

Question

I have a probability density function $f(x) = k \cdot 3e^{-3x}$, with $k\ne 0$ constant. I saw someone saying this is the exponential distribution with $\lambda = 3$. However, isn't the exponencial distribution of the form $\lambda e^{-\lambda x}$? Doesn't the multiplication by a constant change the distribution? Or it just doesn't matter if I multiply it by any value I want?

Answer 1

Hint: consider the equation $1 = \int_0^{\infty} k \cdot 3e^{-3x}dx$.