Change in Tandem is about understanding how input and output values of a function relate.
Mechanistically, it involves examining how a function maps each input to a specific output, ensuring each input has a unique output.
This is described by the function rule, which can be expressed in various forms: graphically, numerically, analytically, or verbally.
The behavior of a function is categorized by intervals where it is increasing or decreasing.
For an increasing function, as input values rise, output values also rise.
Conversely, for a decreasing function, as input values rise, output values fall.
The challenge here is not in solving equations but interpreting these relationships accurately.
You might assume that a function's behavior is uniform across its domain, but it can change dramatically at different intervals.
Misreading these shifts can lead to incorrect conclusions about the function's overall behavior, especially when dealing with complex functions where behavior isn't immediately obvious.