1. The problem is to create the graph of a function of the form $y = a^x$ where $a > 0$ and $a \neq 1$. 2. The general formula for an exponential function is: $$y = a^x$$ where $a$ is the base and $x$ is the exponent. 3. Important rules for exponential functions: - The base $a$ must be positive and not equal to 1. - The function passes through the point $(0,1)$ because $a^0 = 1$. - The function is increasing if $a > 1$ and decreasing if $0 < a < 1$. 4. To graph this function, you plot points for various values of $x$ and connect them smoothly. 5. For example, if $a = 2$, the function is $y = 2^x$. - When $x = -2$, $y = 2^{-2} = \frac{1}{4}$. - When $x = -1$, $y = 2^{-1} = \frac{1}{2}$. - When $x = 0$, $y = 1$. - When $x = 1$, $y = 2$. - When $x = 2$, $y = 4$. 6. Plot these points and draw a smooth curve through them to get the graph of $y = 2^x$. Final answer: The graph of $y = 2^x$ is an exponential curve passing through $(0,1)$, increasing as $x$ increases, and approaching zero as $x$ decreases.