Domain Of A Graph With A Hole

The domain of the function is all real numbers except x 3 x 3.

Domain of a graph with a hole. Domain of a rational function with hole let y f x be a function. There is no vertical asymptote there. In interval notation the domain is 1973 2008 and the range is about 180 2010.

The y value of the hole can be found by canceling the factors and substituting x c in the reduced function. A graph of this function confirms that the function is not defined when x 3 x 3. The only difference between the slant asymptote of the rational function and the rational function itself is that the rational function isn t defined at x 2 to account for this i leave a nice big open circle at the point where x 2 showing that i know that this point is not actually included on the graph because of the zero in the denominator of the rational.

The function is not defined for x 1. You da real mvps. Another way to identify the domain and range of functions is by using graphs.

So the domain is x ℝ x 1 or 1 1. Notice that this graph has one endpoint at 0 0 and an arrow to the right indicating that it continues forever in the positive x direction. So the graph is a linear one with a hole at x 1.

Use the graph to identify the domain and the range. X 0 remember to focus on left to right of the graph for domain of a continuous graph. 1 per month helps.

Analysis of the solution. Thanks to all of you who support me on patreon. Page 1 page 2 asymptotes an asymptote is a line that a graph approaches without touching.