Question

The graph of a piece wise function is shown.

What is the end behavior of the function?

As x → −∞, f(x) → −∞ and as x → ∞, f(x) → −∞.
As x → −∞, f(x) → ∞ and as x → ∞, f(x) → ∞.
As x → −∞, f(x) → ∞ and as x → ∞, f(x) → −∞.
As x → −∞, f(x) → −∞ and as x → ∞, f(x) → ∞.

Answer 1

As x → −∞, f(x) → −∞ and as x → ∞, f(x) → ∞.

Explanation:

The end behavior of a function describes the behavior of the graph as x approaches positive and negative infinity.

From inspection of the graph, as x approaches negative infinity, the function also approaches negative infinity:

• As x → -∞, f(x) → -∞.

As x approaches positive infinity, the function also approaches positive infinity.

• As x → ∞, f(x) → ∞.

Answer 2

• D) As x → −∞, f(x) → −∞ and as x → ∞, f(x) → ∞

Explanation:

The function is not continuous but it behaves as increasing function.

Its ends are on the third and the first quadrants.

It means the last option is the correct one:

• As x → −∞, f(x) → −∞ and as x → ∞, f(x) → ∞