1. The problem is to solve the equation $y = a^x$ where $a > 0$ and $a \neq 1$, and to graph it. 2. The general form of an exponential function is $y = a^x$, where $a$ is the base and $x$ is the exponent. 3. Important rules: - If $a > 1$, the function is increasing. - If $0 < a < 1$, the function is decreasing. - The graph always passes through the point $(0,1)$ because $a^0 = 1$. 4. To graph $y = a^x$, plot points for various values of $x$ and connect them smoothly. 5. For example, if $a = 2$, points include $(0,1)$, $(1,2)$, $(2,4)$, $(-1, \frac{1}{2})$, $(-2, \frac{1}{4})$. 6. The graph has no x-intercepts and the y-intercept is at $(0,1)$. 7. The function has no extrema (no maximum or minimum points). Final answer: The function $y = a^x$ with $a > 0$ and $a \neq 1$ is an exponential function with the properties described above and its graph passes through $(0,1)$, increasing if $a > 1$ and decreasing if $0 < a < 1$.