1. Let's start by understanding what an exponential function is. An exponential function has the form $$y = a^x$$ where $a$ is a positive constant not equal to 1, and $x$ is the exponent. 2. Important rules for exponential functions: - The base $a$ must be greater than 0 and not equal to 1. - The function grows rapidly if $a > 1$ and decays if $0 < a < 1$. - The domain of $y = a^x$ is all real numbers, and the range is positive real numbers. 3. Example: Consider the function $$y = 2^x$$. - When $x=0$, $y=2^0=1$. - When $x=1$, $y=2^1=2$. - When $x=-1$, $y=2^{-1}=\frac{1}{2}$. 4. Exponential growth means the function increases as $x$ increases, and exponential decay means it decreases as $x$ increases. 5. To solve problems involving exponential functions, you often use logarithms to find $x$ when $y$ is known, or evaluate the function for given $x$ values. This is the basic introduction to exponential functions to help you study further.