Exponential Function Student Activity: Graphing And Analysis.pdf

## Exponential Function Student Activity Summary

This activity investigates the behavior of exponential functions through data tables, graphing, and analysis.

1. Data Table & Graph:

Table: Students calculate values for 2x and 5x using a base value (presumably 2 or 5) and an exponent (values of x from -4 to 4).
Graph: The data points are plotted, revealing a curve that approaches but never touches the x-axis.

1.c & 1.d Analysis:

The graph exhibits exponential growth because the difference between consecutive y values increases exponentially as x increases (or decreases). This is characteristic of exponential functions, where the rate of change is proportional to the current value. Therefore, it is an example of an exponential function.

2. Repeat Activity with Different Base:

* Table & Graph: Students repeat the process with a new base value (e.g., 3) and observe the effect on the graph's shape.

2.c & 2.d Analysis:

For values of x less than one, the graph approaches the x-axis from above. This indicates that as x gets smaller, the exponential term becomes smaller relative to the base, causing the curve to flatten out. The graph never touches the x-axis because even with decreasing x values, the y values continue to be positive due to the exponential nature of the function.

2.e Analysis:

Again, based on the characteristic behavior (exponential growth), this graph is also an example of an exponential function.