Question

Describe the vertical asymptote (s) and hole (s) for the graph of y = (x+2) (x+4)/ (x+4) (x+1)

Answer 1

Given:

`y=((x+2)(x+4))/((x+4)(x+1))`

Required:

We need tofnind the vertical asymptote(s) and hole (s) for the graph of the given function.

Step-by-step explanation:

Vertical asymptotes can be found when the numerator of the function is equal to zero.

The numerator of the given function is (x+4)(x+1)

`(x+4)(x+1)=0`

`(x+4)=0\text{ or }(x+1)=0`
`x=-4\text{ or x=-1}`

The asymptote of the given function is either x =-4 or x =-1.

Recall that a hole exists on the graph of a rational function when both the numerator and denominator of the function are equal to zero.

The common factor of the given rational function