Question

Where should I place the hollow point in this graph?

Answer 1

Hollow point is a point in which the function is undefined.

The function is undefined if the denominator is equal to 0.

From the problem, we have the function :

`h(x)=(3x+15)/(x^2+7x+10)`

Equate the denominator to 0.

`x^2+7x+10=0`

Then factor completely :

`\begin{gathered} (x+5)(x+2)=0 \\ \text{Solve for the values of x :} \\ x+5=0 \\ x=-5 \\ \\ x+2=0 \\ x=-2 \end{gathered}`

The values of x that will make the function undefined are x = -2 and -5

From the graph, the asymptote is located at x = -2, so we will put the hollow point at the other value of x which is x = -5

ANSWER :

Locate the hollow point at x = -5.

It will be :