1. The problem is to find the range of a function $f(x)$, which means determining all possible output values of $f(x)$ for all $x$ in the domain. 2. To find the range, we often start by understanding the function type (linear, quadratic, rational, etc.) and its behavior. 3. For example, if $f(x)$ is a quadratic function $f(x) = ax^2 + bx + c$, the range depends on the vertex and whether the parabola opens up or down. 4. The vertex form is $f(x) = a(x-h)^2 + k$, where $(h,k)$ is the vertex. 5. If $a > 0$, the parabola opens upward and the range is $[k, \infty)$. 6. If $a < 0$, the parabola opens downward and the range is $(-\infty, k]$. 7. For other functions, analyze critical points, asymptotes, and limits to determine the range. 8. Without a specific function, the general approach is to find all $y$ such that $y = f(x)$ has at least one solution $x$. Final answer: The range depends on the specific function $f(x)$ and is the set of all possible output values of $f(x)$.