Question

Which of the following is the function for the graph below and shows the end behavior of the function as x⟶ -∞?

f(x) = (3x2 - x + 2)(x + 2); f(x) ⟶ +∞
f(x) = (3x2 - x + 2)(x - 2); f(x) ⟶ -∞
f(x) = (3x2 - x - 2)(x + 2); f(x) ⟶ -∞
f(x) = (3x2 - x - 2)(x - 2); f(x) ⟶ +∞

Answer 1

"x⟶ -∞" indicates that we are moving to the left (towards negative infinity). This automatically eliminates the first and fourth answer choices.

Look carefully at the graph. We see immediately that one of the zeros is x=-2. The corresponding factor of the polynominal representing the graph would then be (x+2). Thus, the correct answer choice is:

f(x) = (3x2 - x - 2)(x + 2); f(x) ⟶ -∞