# How do I use the graph of a function to predict future behavior?

Well, this is a difficult one! I am not sure this is going to help, but I try anyway.

When I have to analyze a phenomenon (I am a physicist...!) I collect data that characterize the phenomenon (for example, I measure the height of a kid each week) and then I plot them.

The result is a graph with points on it that hopefully shows a "tendency".

(hope it helps!)

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By examining the graph of a function, you can make predictions about its future behavior by analyzing its overall shape, critical points, and long-term trends. This includes:

- Identifying asymptotes, both horizontal and vertical, which can indicate the behavior of the function as ( x ) approaches certain values or infinity.
- Observing the concavity of the function and the locations of inflection points to understand how the function curves.
- Examining the end behavior of the function as ( x ) approaches positive or negative infinity to determine if it grows without bound, approaches a finite limit, or oscillates.
- Noticing any periodic behavior or patterns, if applicable, which can help predict recurring trends.
- Analyzing the slope of the function at various points to understand the rate of change and whether it is increasing, decreasing, or remaining constant.
- Considering any discontinuities or singularities in the graph and their implications for the function's behavior.

By carefully interpreting these features of the graph, you can make informed predictions about the function's behavior beyond the observed data points or interval of interest.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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