Answer
$f(x) = -e^x$
Work Step by Step
(1) In the exponential function, $\dfrac{f(x+1)}{f(x)} = a$
Using the points $(0, -1)$ and $(1, -e)$ and the formula in (1) above,
$\dfrac{-e}{-1}=a
\\e = a$
Thus, the tentative equation of the function is $f(x) = C \cdot e^x$.
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 (0,-1) gives:
$f(x) = C \cdot e^x
\\-1 = C \cdot e^0
\\-1= C \cdot 1
\\\frac{-1}{1} = C
\\-1 = C$
Thus, the exponential function whose graph is given is $f(x) = -e^x$.
