Question
Describe the end behavior of the function below.
the main points are (0,-5) (0.5,0) (1.5,4) (2.5,0)
(2 points)
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As x approaches −∞, f(x) approaches
Response area.
As x approaches ∞, f(x) approaches
the main points are (0,-5) (0.5,0) (1.5,4) (2.5,0)
(2 points)
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
Response area.
As x approaches ∞, f(x) approaches
Answers
Answered by
GPT-4o mini
To determine the end behavior of the function based on the points given:
1. As \( x \) approaches \( -\infty \), we look to see where the function is likely heading. Since we have no information about points to the left of \( (0, -5) \), we cannot definitively say what \( f(x) \) approaches; however, given that the closest point is \( (0, -5) \), we can speculate that it may continue to decrease or stay at a certain value.
2. As \( x \) approaches \( \infty \), we examine the provided points: \( (0.5, 0) \), \( (1.5, 4) \), and \( (2.5, 0) \). Notice that it appears the function rises to \( (1.5, 4) \) and then returns back to \( (2.5, 0) \). This suggests that after reaching a peak, the function returns to 0. Thus, we can conclude that as \( x \) increases beyond \( (2.5, 0) \), if we follow similar patterns, it likely will continue to approach 0. However, without further context, we can't make a solid prediction.
In summary, we write the responses as follows:
As \( x \) approaches \( -\infty \), \( f(x) \) approaches **undefined or a decreasing behavior may be assumed**.
As \( x \) approaches \( \infty \), \( f(x) \) approaches **0**.
1. As \( x \) approaches \( -\infty \), we look to see where the function is likely heading. Since we have no information about points to the left of \( (0, -5) \), we cannot definitively say what \( f(x) \) approaches; however, given that the closest point is \( (0, -5) \), we can speculate that it may continue to decrease or stay at a certain value.
2. As \( x \) approaches \( \infty \), we examine the provided points: \( (0.5, 0) \), \( (1.5, 4) \), and \( (2.5, 0) \). Notice that it appears the function rises to \( (1.5, 4) \) and then returns back to \( (2.5, 0) \). This suggests that after reaching a peak, the function returns to 0. Thus, we can conclude that as \( x \) increases beyond \( (2.5, 0) \), if we follow similar patterns, it likely will continue to approach 0. However, without further context, we can't make a solid prediction.
In summary, we write the responses as follows:
As \( x \) approaches \( -\infty \), \( f(x) \) approaches **undefined or a decreasing behavior may be assumed**.
As \( x \) approaches \( \infty \), \( f(x) \) approaches **0**.