Answer
$f(x) = -6^x$
Work Step by Step
The exponential function has the form: $\dfrac{f(x+1)}{f(x)} = a(1)$
We will use the points $(1, -6)$ and $(2, -36)$ in equation (1) to obtain: $\dfrac{-36}{-6}=a \implies a=6$
Thus, we can write the equation of the function as: $f(x) = C \cdot 6^x$.
In order to compute the value of $C$, we will apply the point $x=1; y=f(x)=-6$ as follows:
$-6 = C \times 6^{(1)} \\C= \dfrac{-6}{6} \\ C=-1$
Therefore, the required exponential function is of the form:
$f(x) = -6^x$
