Question

a) Find the function algebraically. Show yourwork!b) Where is the asymptote on the graph of thisfunction? Give as an equation.c) What is the domain and range of thisfunction?Domain:Range:

Answer 1

(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:

`\begin{gathered} f(x)=a^x \\ \\ (-3,8)\colon \\ 8=a^(-3) \\ 2^3=((1)/(a))^3 \\ 2=(1)/(a) \\ a=(1)/(2) \end{gathered}`

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)