1. The problem is to graph the function $y = a^x$ where $a > 0$ and $a \neq 1$. 2. The general form of an exponential function is $y = a^x$. 3. Important rules: - If $a > 1$, the function is increasing. - If $0 < a < 1$, the function is decreasing. - The graph passes through the point $(0,1)$ because $a^0 = 1$. - The $x$-axis ($y=0$) is a horizontal asymptote. 4. To graph, plot points for various $x$ values and connect smoothly. 5. Example: For $a=2$, points are $(0,1)$, $(1,2)$, $(2,4)$, $(-1, \frac{1}{2})$, $(-2, \frac{1}{4})$. 6. The graph rises rapidly for positive $x$ and approaches zero for negative $x$. Final answer: The graph of $y = a^x$ with $a > 0$ and $a \neq 1$ is an exponential curve passing through $(0,1)$, increasing if $a > 1$, decreasing if $0 < a < 1$, with horizontal asymptote $y=0$.