(a)
In order to find the function, let's use the ordered pair (-3, 8) in the given exponential function f(x).
So we have:
[tex]\begin{gathered} f(x)=a^x \\ \\ (-3,8)\colon \\ 8=a^{-3} \\ 2^3=(\frac{1}{a})^3 \\ 2=\frac{1}{a} \\ a=\frac{1}{2} \end{gathered}[/tex]
So the function is f(x) = (1/2)^x
(b)
The asymptote of this graph is y = 0, that is, the horizontal axis.
(c)
The domain is the values that x can assume, so the domain of this function is all real numbers, that is, (-infinity, infinity)
The range is the values that f(x) can assume, so the range of this function is y>0, that is, all positive numbers: (0, infinity)
