Question

which statement is true about the end behavior of the graphed function?
as the x - values go to positive infinity, the functions values go to negative infinity
as the x - values go to zero, the functions values go to positive infinity.
as the x - values go to negative infinity, the functions values are equal to zero
as the x - values go to negative infinity, the functions values go to positive infinity

Explanation:

End behavior refers to the function's trend as \(x\) approaches \(+\infty\) or \(-\infty\). Observing the graph:

• When \(x\) goes to positive infinity (right end), the function values rise sharply to positive infinity, so the first option is false.
• The question about \(x\) going to zero is not end behavior (end behavior is about infinity), so the second option is irrelevant.
• When \(x\) goes to negative infinity (left end), the function values rise sharply to positive infinity, not zero, so the third option is false.
• The fourth option correctly describes the left end behavior: as \(x \to -\infty\), function values go to \(+\infty\).

Answer:

As the x-values go to negative infinity, the function's values go to positive infinity