Answer :
The correct local and end behaviors include;
A. As x → 2⁻, f(x) → ∞.
B. As x → -∞, f(x) → -1.
E. As x → 2⁺, f(x) → -∞.
The end behavior of a function describes what happens when x approaches infinity, or the right side of the graph, and what happens when x approaches negative infinity or the left side of the graph.
By critically observing the graph of the rational function shown above, the local behaviors are as follows;
As x tends towards 2 from the left, f(x) tends towards positive infinity i.e As x → 2⁻, f(x) → ∞.
As x tends towards 2 from the right, f(x) tends towards negative infinity i.e As x → 2⁺, f(x) → -∞.
For the end behavior of the graph, we have;
As x tends towards negative infinity, f(x) tends towards negative one i.e As x → -∞, f(x) → -1.
As x tends towards positive infinity, f(x) tends towards negative one i.e As x → +∞, f(x) → -1.
