Question

the graph of ( y = f(x) ) is graphed below. what is the end behavior of ( f(x) )?
answer
( circ ) as ( x \to -infty, y \to infty ) and
( quad ) as ( x \to infty, y \to infty )
( circ ) as ( x \to -infty, y \to -infty ) and
( quad ) as ( x \to infty, y \to -infty )
( circ ) as ( x \to -infty, y \to -infty ) and
( quad ) as ( x \to infty, y \to infty )
( circ ) as ( x \to -infty, y \to infty ) and
( quad ) as ( x \to infty, y \to -infty )

Explanation:

To determine the end - behavior of the function \(y = f(x)\) from its graph, we analyze the direction of the graph as \(x\) approaches positive infinity (\(x
ightarrow\infty\)) and negative infinity (\(x
ightarrow-\infty\)).

• When \(x

ightarrow-\infty\): We look at the left - hand side of the graph. From the given graph, as \(x\) moves towards \(-\infty\) (to the left), the graph of the function is going upwards, which means \(y
ightarrow\infty\).

• When \(x

ightarrow\infty\): We look at the right - hand side of the graph. As \(x\) moves towards \(\infty\) (to the right), the graph of the function is also going upwards, which means \(y
ightarrow\infty\).

Among the given options, the one that matches this end - behavior is "as \(x
ightarrow-\infty,y
ightarrow\infty\) and as \(x
ightarrow\infty,y
ightarrow\infty\)".

Answer:

as \(x \to -\infty, y \to \infty\) and as \(x \to \infty, y \to \infty\)