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# 1: Functions

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• 1.1: Functions and Function Notation
• 1.2: Domain and Range
One of our main goals in mathematics is to model the real world with mathematical functions. In doing so, it is important to keep in mind the limitations of those models we create.
• 1.3: Rates of Change and Behavior of Graphs
Since functions represent how an output quantity varies with an input quantity, it is natural to ask about the rate at which the values of the function are changing.
• 1.4: Composition of Functions
• 1.5: Transformation of Functions
There are systematic ways to shift, stretch, compress, flip and combine functions to help them become better models for the problems we are trying to solve. We can transform what we already know into what we need, hence the name, “Transformation of functions.” When we have a story problem, formula, graph, or table, we can then transform that function in a variety of ways to form new functions.
• 1.6: Inverse Functions