Final answer:
To describe a transformation from one function to another, one must analyze how different manipulations, such as altering the slope or intercept, affect the function's representation, such as tilting or shifting a line on a graph.
Step-by-step explanation:
To describe a transformation from one function to another, we consider how the output of a function changes based on the manipulation of its input or its equation. A function in mathematics defines a particular relationship between variables where each input is associated with exactly one output. For example, the relationship, represented by Professor = Adam Smith, could be considered a function where the 'Professor' variable is assigned the value 'Adam Smith'.
When transforming one function to another, we might change one or more characteristics of the function such as its slope, intercept, or other parameters. For instance, the equation of a line y = mx + b has a slope (m) and an intercept (b). Changing the slope will tilt the line, while changing the intercept will shift it up or down on the graph. If we change the slope of a line from 2 to 3, then the new line will be steeper.
Growth rates, often expressed as percentage changes, can also be considered functions. These describe how a quantity changes over time. Being able to compute, interpret, and manipulate these functions is vital for understanding and modeling economic, physical, or scientific phenomena.