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 positive infinity, the functions values go to positive infinity.

Explanation:

Step1: Analyze the end - behavior as \(x\to+\infty\)

Looking at the right - hand side of the graph (as \(x\) increases), we observe the direction of the function. As \(x\) goes to positive infinity (\(x\to+\infty\)), we check if the \(y\) - values (function values) go to positive or negative infinity.

Step2: Analyze the end - behavior as \(x\to-\infty\)

Looking at the left - hand side of the graph (as \(x\) decreases), we observe the direction of the function. As \(x\) goes to negative infinity (\(x\to-\infty\)), we check if the \(y\) - values (function values) go to positive or negative infinity.

Step3: Analyze the behavior as \(x\to0\)

We also check the behavior of the function near \(x = 0\).

For the given graph:

• As \(x\to+\infty\), the function values (\(y\)) go to negative infinity.
• As \(x\to0\), the function values are finite (not going to positive infinity).
• As \(x\to-\infty\), the function values are not zero.

Answer:

As the \(x\) - values go to positive infinity, the function’s values go to negative infinity.