the graph of a rational function, f, is shown in the figure.\nuse the graph to find the domain and range of…

the graph of a rational function, f, is shown in the figure.\nuse the graph to find the domain and range of f.\n\nwhat is the domain of f?\n(type your answer in interval notation.)

the graph of a rational function, f, is shown in the figure.\nuse the graph to find the domain and range of f.\n\nwhat is the domain of f?\n(type your answer in interval notation.)

Answer

Explanation:

Step1: Identify vertical asymptotes

The graph has vertical dashed lines (asymptotes) at $x=-4$ and $x=6$, so these $x$-values are excluded from the domain.

Step2: Define domain intervals

The function exists for all real numbers except $x=-4$ and $x=6$. This splits the domain into three intervals: $(-\infty, -4)$, $(-4, 6)$, and $(6, \infty)$.

Answer:

$(-\infty, -4) \cup (-4, 6) \cup (6, \infty)$