Question

What is the function shown in the graph:

Answer 1

A. f(x)=1/x+1
B. f(x)= x+1/x^2+3x+2
C. f(x)= x+2
D. f(x)= x^2+3x+2/x+1

Answer 2

Since there is a break at x=-1, you know that at some point there must be a divide by 0. The function is otherwise linear so you need a rational function with a numerator whose degree is one larger than its denominator.

The only answer where this is the case is D.

To prove it, you can factor out the numerator x^2+3x+2 into (x+2)(x+1)

Notice how there is also an x+1 in the denominator. those cancel, but in order to keep the function the same, you must ensure that you keep the x=/= -1 (as that would result in a divide by zero.

Hence, the function x^2+3x+2/x+1 simplifies to x+2; x=/=0

Answer 3

Oh okay thank you for explaining! (: