The graph y=f(x) is graphed below. What is the end behavior of f(x)?

The end behavior of a graph is defined as what is going on at the ends of each graph when the function approaches positive or negative infinity.

End behaviour of given graph is,  x⇒ -∞ then y⇒∞ and x ⇒∞ then y⇒ -∞

Since, here a  graph is attached.

From graph it is observed that, when x tends to negative side, graph is going to upward direction. and when x tends to positive side then graph is going to downward direction.

So, when  x tends negative infinity then y tends to positive infinity.

when x tends to positive infinity then y tends to negative infinity.

Therefore, end behaviour of given graph are,

                    x⇒ -∞ then y⇒∞ and x ⇒∞ then y⇒ -∞

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as x → -∞, y → ∞ and as x → ∞, y → -∞

Step-by-step explanation:

Just check the first quadrant of the given graph.

In the first quadrant, when x gets smaller, the value of y is increasing to positive infinity.

In other words, as x → -∞, y → ∞

Now, observe the behavior of the graph in the 4th quadrant.

In the 4th quadrant, when x gets larger, the value of y is decreasing to negative infinity.

In other words, as x → ∞, y → -∞

Therefore, the behavior of f(x):

as x → -∞, y → ∞ and as x → ∞, y → -∞

Therefore, option (C) is true.

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