consider the table representing a rational function.\n|x| - 0.1| - 0.01| - 0.001|0|0.001|0.01|0.1|2.9|3|3.1|4…

consider the table representing a rational function.\n|x| - 0.1| - 0.01| - 0.001|0|0.001|0.01|0.1|2.9|3|3.1|4.9|4.99|5|5.001|5.01|5.1|\n|f(x)|1.96|19.96|199.96|undefined| - 200.04| - 20.04| - 2.04| - 0.16|undefined| - 0.17| - 2.04| - 20.04|undefined|199.96|19.96|1.96|\nwhich statement describes the graph of the function?\no the function has holes when x = 0, x = 3, and x = 5.\no the function has vertical asymptotes when x = 0, x = 3, and x = 5.\no the function has holes when x = 0 and x = 3, and a vertical asymptote when x = 5.\no the function has a hole when x = 3, and vertical asymptotes when x = 0 and x = 5.

consider the table representing a rational function.\n|x| - 0.1| - 0.01| - 0.001|0|0.001|0.01|0.1|2.9|3|3.1|4.9|4.99|5|5.001|5.01|5.1|\n|f(x)|1.96|19.96|199.96|undefined| - 200.04| - 20.04| - 2.04| - 0.16|undefined| - 0.17| - 2.04| - 20.04|undefined|199.96|19.96|1.96|\nwhich statement describes the graph of the function?\no the function has holes when x = 0, x = 3, and x = 5.\no the function has vertical asymptotes when x = 0, x = 3, and x = 5.\no the function has holes when x = 0 and x = 3, and a vertical asymptote when x = 5.\no the function has a hole when x = 3, and vertical asymptotes when x = 0 and x = 5.

Answer

Brief Explanations:

A hole in a rational - function occurs when a factor in the numerator and denominator cancels out. A vertical asymptote occurs when the denominator of a rational function is zero and the numerator is non - zero at that point. Looking at the table, the function is undefined at (x = 0), (x=3), and (x = 5). As (x) approaches (0) and (5) from both sides, the function values approach positive or negative infinity, which indicates vertical asymptotes. As (x) approaches (3), the function values approach a finite value (around (- 0.16) and (-0.17)), which indicates a hole.

Answer:

The function has a hole when (x = 3), and vertical asymptotes when (x = 0) and (x = 5).