Question

Which function is an extended function

Answer 1

D. The last option

Step-by-step explanation:

You can't divide by 0, so find out when the given function is discontinuous.

`(x^3+3x^2-x-3)/(x^2-1) =(x^3+3x^2-x-3)/((x+1)(x-1))`

You can see that x is discontinuous at x=-1,1, so find a piecewise function that fill in those gaps.

Plug x=-1,1 into your function to find out what values you need to fill in. But of course it's discontinuous at those points, so plug in a number near x=1 and x=-1. I chose x=-1.1 and x=1.1

`f(-1.1)((-1.1)^3+3(-1.1)^2-(-1.1)-3)/((-1.1)^-1) = 1.9 \approx 2`

`f(1.1)((1.1)^3+3(1.1)^2-(1.1)-3)/((1.1)^-1) = 4.1 \approx 4`

so we need to fill in 2 at x=-1, and fill in 4 at x=1