Answer
$f(x) = -6^x$
Work Step by Step
RECALL:
(1) In the exponential function above, $\dfrac{f(x+1)}{f(x)} = a$
Using the points $(1, -6)$ and $(2, -36)$ and the formula in (1) above,
$\dfrac{-36}{-6}=a
\\6 = a$
Thus, the tentative equation of the function is $f(x) = C \cdot 6^x$.
To find the value of $C$, use any point on the graph and substitute the x and y values of the point into the tentative equation above. Using the point (1,-6) gives:
$f(x) = C \cdot 6^x
\\-6 = C \cdot 6^1
\\-6= C \cdot 6
\\\frac{-6}{6} = C
\\-1 = C$
Thus, the exponential function whose graph is given is $f(x) = -6^x$.
