How do you calculate range

For a set of numbers, the range is the difference between the highest and lowest values in the set. Example: For the set $\{2, 5, 8, 1, 10\}$, the highest value is 10 and the lowest is 1. Range $= 10 - 1 = 9$.

For a function, the range is the set of all possible $y$-values (output values) that the function can produce. This often depends on the type of function:

• For a linear function $f(x) = mx+c$ (where $m \neq 0$), the range is typically $(-\infty, \infty)$.
• For a quadratic function $f(x) = ax^2+bx+c$, the range depends on the vertex. If $a>0$, the range is $[y_{vertex}, \infty)$. If $a<0$, the range is $(-\infty, y_{vertex}]$.
• For a rational function like $h(x) = -\frac{3}{x} - 4$ from the previous question, the range is all real numbers except the horizontal asymptote. So, the range is $(-\infty, -4) \cup (-4, \infty)$.