First, notice that the given graph is the reflected over the x-axis and y-axis version of an exponential function of the form:
[tex]y=ab^x.[/tex]
Now, the y-intercept of the graph is -3, therefore, the parent function has
[tex]a=3.[/tex]
Now, the graph passes through the point (-1,-6), therefore, the parent function passes through (1,6). Solving
[tex]6=3(b)^1,[/tex]
for b, we get:
[tex]\begin{gathered} b=\frac{6}{3}, \\ b=2. \end{gathered}[/tex]
Finally, we reflect the parent function over the x-axis and over the y-axis and get:
[tex]y=-3(2)^{-x}.[/tex]
Answer:
[tex]y=-3(2)^{-x}.[/tex]
