Describe how the graph of the function \( f(x) = 2^x \) changes when transformed to \( g(x) = 2^{x-3} \).

The population of a town is currently 20,000 and is growing at a rate of 5% per year. Write an exponential function that models the population growth over time.

Find the vertical asymptotes, if any, of the graph of the rational function. \( f(x)=\frac{x}{x^{2}+8} \)

Find the horizontal asymptote, if any, of the graph of the rational function. \( g(x)=\frac{9 x^{2}}{3 x^{2}+1} \)

यदि \( g(x) = 2^{x} \), तो इसके इनवर्स फ़ंक्शन की पहचान करें और उसका डोमेन तथा रेंज लिखिए।

1. \( f(x)=x+\frac{1}{x} \rightarrow f(1), f(-1), f(2), f\left(\frac{1}{2}\right) \)