Question

What is the graph of the function f(x)= x^2+5x+6/x+3?

Answer 1

`y =(x^2+5x+6)/(x+3) \qquad \text{Restriction: x}\\eq -3`

`y =((x+3)(x+2))/(x+3) \qquad \text{Restriction: x}\\eq -3`

`y = x + 2 \qquad \text{Restriction: x}\\eq -3`

Restriction: when x = -3, y = (-3) + 2

= -1

So, there is a hole at (-3, -1)

The graph has a y-intercept of 2, a slope of 1, and a hole (-3, -1)

(See attached graph)