1. The problem is to draw the graph of the function $f(x) = 4^x$. 2. The function $f(x) = a^x$ where $a > 0$ and $a \neq 1$ is an exponential function. 3. Important properties of exponential functions: - The graph passes through the point $(0,1)$ because $a^0 = 1$. - The function is always positive, so $f(x) > 0$ for all $x$. - The function increases if $a > 1$ and decreases if $0 < a < 1$. 4. For $f(x) = 4^x$, since $4 > 1$, the function is increasing. 5. To plot, calculate some points: - $f(-2) = 4^{-2} = \frac{1}{16} = 0.0625$ - $f(-1) = 4^{-1} = \frac{1}{4} = 0.25$ - $f(0) = 4^0 = 1$ - $f(1) = 4^1 = 4$ - $f(2) = 4^2 = 16$ 6. Plot these points and draw a smooth curve through them, approaching the x-axis as $x \to -\infty$ and increasing rapidly as $x \to \infty$. Final answer: The graph of $f(x) = 4^x$ is an increasing exponential curve passing through $(0,1)$, approaching zero for negative $x$, and growing rapidly for positive $x$.