1. The problem is to graph the function $f(x) = x^4$. 2. This is a polynomial function where the variable $x$ is raised to the fourth power. 3. The graph of $f(x) = x^4$ is a curve that is symmetric about the y-axis because the exponent is even. 4. The function has a minimum point at the origin $(0,0)$ since $x^4 \geq 0$ for all real $x$. 5. As $x$ moves away from zero in either direction, $f(x)$ increases rapidly because raising to the fourth power grows quickly. 6. The graph looks like a very steep "U" shape, steeper than $x^2$ because of the higher power. Final answer: The graph of $f(x) = x^4$ is a symmetric curve with a minimum at $(0,0)$ and increases steeply as $|x|$ increases.