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?\nthe function has holes when x = 0, x = 3, and x = 5.\nthe function has vertical asymptotes when x = 0, x = 3, and x = 5.\nthe function has holes when x = 0 and x = 3, and a vertical asymptote when x = 5.\nthe 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?\nthe function has holes when x = 0, x = 3, and x = 5.\nthe function has vertical asymptotes when x = 0, x = 3, and x = 5.\nthe function has holes when x = 0 and x = 3, and a vertical asymptote when x = 5.\nthe function has a hole when x = 3, and vertical asymptotes when x = 0 and x = 5.

Answer

Explanation:

Step1: Analyze function values near x - values

When the function value approaches infinity or negative - infinity as x approaches a certain value, it indicates a vertical asymptote. When the function is undefined at a point but the limit exists at that point, it indicates a hole.

Step2: Check x = 0

As x approaches 0 from the left (-0.1, -0.01, -0.001), f(x) increases rapidly (1.96, 19.96, 199.96). As x approaches 0 from the right (0.001, 0.01, 0.1), f(x) decreases rapidly (-200.04, -20.04, -2.04). So, x = 0 is a vertical asymptote.

Step3: Check x = 3

The function is undefined at x = 3, but the values of f(x) on either side of x = 3 (-0.16 on the left and -0.17 on the right) are relatively close. This indicates a hole at x = 3.

Step4: Check x = 5

As x approaches 5 from the left (4.9, 4.99), f(x) decreases rapidly (-2.04, -20.04). As x approaches 5 from the right (5.001, 5.01), f(x) increases rapidly (199.96, 19.96). So, x = 5 is a vertical asymptote.

Answer:

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