Exercise 2 Page 70

To determine which of the sentences best describes the end behavior, we have to understand what it means to say that $x$ and $y$ are increasing or decreasing.

• An increasing value of $x$ means that we are moving to the right on the coordinate plane. This means that the $x\text{-}$values are getting bigger.
• A decreasing value of $x$ means that we are moving to the left on the coordinate plane. This means that the $x\text{-}$values are getting smaller.
• An increasing value of $y$ means that the graph is moving upwards on the coordinate plane. Therefore, the $y\text{-}$values are getting bigger.
• A decreasing value of $y$ means that the graph is moving downwards on the coordinate plane. Therefore, the $y\text{-}$values are getting smaller.

Now, let's look at the given graph. Pay close attention to the behavior of the variable $y$ when $x$ is increasing.

Looking at the rightmost side of the function, we can see that as $x$ is increasing, the $y\text{-}$values are decreasing. This behavior matches statements H and J. To determine which of these choices is correct, let's look at the behavior of $y$ as $x$ is decreasing.

This time we need to look at the leftmost side of the function. As $x$ is decreasing, the $y\text{-}$values are increasing. Therefore, we disregard choice J. The correct choice is H.