Use the graph to determine which statement is true about the end behavior of f(x).

Question

As the x-values go to negative infinity, the function’s values go to negative infinity.
As the x-values go to negative infinity, the function’s values go to positive infinity.
As the x-values go to positive infinity, the function’s values go to negative infinity.
As the x-values go to positive infinity, the function’s values go to zero.

Answer 1

To determine the end behavior of the function \( f(x) \) based on the graph, we need to look at how the function's values behave as the \( x \)-values approach negative infinity and positive infinity.

Here are the steps you should follow:

1. **Observing \( f(x) \) as \( x \) approaches negative infinity:**
- Look at the left end of the graph.
- Determine if the function is increasing, decreasing, or leveling off.

2. **Observing \( f(x) \) as \( x \) approaches positive infinity:**
- Look at the right end of the graph.
- Determine if the function is increasing, decreasing, or leveling off.

By analyzing these aspects, we can match your observations with the given statements. Since I can't see the graph, I'll explain the decisions for each statement:

1. **As the \( x \)-values go to negative infinity, the function’s values go to negative infinity.**
- This means the left end of the graph is sloping downwards.

2. **As the \( x \)-values go to negative infinity, the function’s values go to positive infinity.**
- This means the left end of the graph is sloping upwards.

3. **As the \( x \)-values go to positive infinity, the function’s values go to negative infinity.**
- This means the right end of the graph is sloping downwards.

4. **As the \( x \)-values go to positive infinity, the function’s values go to zero.**
- This means the right end of the graph is approaching the x-axis (leveling off around y = 0).

By matching these descriptions with the actual graph you're observing, you can determine which statements are true. Graphs of common functions such as polynomials, exponentials, and logarithmic functions often follow these end behaviors, so understanding the shape and direction of the graph will help you choose the correct statement.