Question

Describe the end behavior of the function below. (2 points)
Graph:
1.5,4
0.5,0
2.5,0
0,-5
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. As x approaches −∞, f(x) approaches As x approaches −∞, f(x) approaches Response area. As x approaches ∞, f(x) approaches As x approaches ∞, f(x) approaches Response area. −∞−∞∞∞0-5

Answer 1

To determine the end behavior of the function based on the given points, we can look at the points you've provided and infer how f(x) behaves as x approaches negative infinity (−∞) and positive infinity (∞).

The points given are:
1. (1.5, 4)
2. (0.5, 0)
3. (2.5, 0)
4. (0, -5)

From these points, we can analyze the end behavior:

1. **As x approaches -∞**: It looks like the function starts from the point (0, -5). There are no points provided that imply the function goes up or down further in the negative direction of x. Therefore, we can infer:
- As x approaches −∞, f(x) approaches −∞.

2. **As x approaches ∞**: The provided points do not indicate any bounds on the function as x increases, but we can see that the point (1.5, 4) suggests that the function reaches a value of 4 after (0.5, 0) is crossed, and the last point (2.5, 0) indicates a return to 0 after reaching another height. This suggests variability but we can't discern a limit going to positive values as x increases without more information. Assuming typical behaviors of polynomials, if the function rises, we might conclude:
- As x approaches ∞, f(x) approaches ∞.

Therefore, the end behavior can be summarized as:

- As x approaches −∞, f(x) approaches **−∞**.
- As x approaches ∞, f(x) approaches **∞**.