representing a function with a graph\nwhich graph represents the function $f(x)=(\frac{3}{2})^{-x}$

Explanation:

Step1: Rewrite the function

We can rewrite $f(x)=(\frac{3}{2})^{-x}$ as $f(x)=(\frac{2}{3})^{x}$ using the negative - exponent rule $a^{-n}=\frac{1}{a^{n}}$.

Step2: Analyze the exponential - function form

The general form of an exponential function is $y = a^{x}$, where $a>0,a\neq1$. When $0 < a<1$, the function is a decreasing exponential function. Here $a = \frac{2}{3}\in(0,1)$.

Step3: Check the y - intercept

When $x = 0$, $y=(\frac{2}{3})^{0}=1$. So the function passes through the point $(0,1)$.

Answer:

The graph that is a decreasing curve and passes through the point $(0,1)$ is the correct one.