Answer:
An exponential decay function [tex]y =ab^x[/tex] where a is the initial value and 0<b<1.
Given the function: [tex]f(x) = (\frac{3}{2})^{-x}[/tex]
or we can write this as;
[tex]y=f(x) = (\frac{2}{3})^{x}[/tex] ......[1]
The domain for this function is all real number and the range is, y>0.
also this function is decreasing because b = [tex]\frac{2}{3}[/tex] < 1.
First find the y-intercept:
y-intercepts defined as the graph crosses the y-axis
substitute x =0 in [1] to find x;
[tex]y = (\frac{2}{3})^{0} = 1[/tex]
y-intercepts: (0, 1).
End behavior of the given function:
as [tex]x \rightarrow \infty[/tex] , [tex]f(x) \rightarrow 0[/tex]
as [tex]x \rightarrow -\infty[/tex] , [tex]f(x) \rightarrow \infty[/tex]
As you can see the graph of this function below in the attachment.
