1. **State the problem:** Graph the exponential function $y=4^x$ by hand and include at least two points on the graph. 2. **Recall the formula:** The general form of an exponential function is $y=a^x$ where $a>0$ and $a \neq 1$. 3. **Important rules:** - When $x=0$, $y=a^0=1$. - For positive $x$, $y$ increases if $a>1$. - For negative $x$, $y$ approaches 0 but never reaches it. 4. **Calculate points:** - At $x=0$, $y=4^0=1$. - At $x=1$, $y=4^1=4$. - At $x=-1$, $y=4^{-1}=\frac{1}{4}$. 5. **Plot points:** The points $(0,1)$, $(1,4)$, and $(-1,\frac{1}{4})$ lie on the graph. 6. **Explain behavior:** The graph passes through $(0,1)$, rises steeply for $x>0$, and approaches the $x$-axis (but never touches it) for $x<0$. **Final answer:** The graph of $y=4^x$ passes through points $(0,1)$ and $(1,4)$ and approaches zero as $x$ becomes negative.