Identify whether each value of x is a discontinuity of the function by typing asymptote, hole, or neither. 5x x3 + 5x2 + 6x

Question

x = −3 

x = −2 

x = 0 

x = 2 

x = 3 

x = 5

Answer 1

I am going to assume you mean (5x)/(x^3 + 5x^2 + 6x) . If so we can factor the denominator and get:

(5x)/([x(x+3)(x+2)] which provides 3 values for which the denominator equals zero: 0, -2, -3

Since we could cancel an x out of both the numerator and denominator, 0 becomes a hole in the graph.

-2 and -3 are vertical asymptotes

2, 3, and 5 are neither