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1.1: Functions and Function Notation
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A function is a rule for a relationship between an input, or independent, quantity and an output, or dependent, quantity in which each input value uniquely determines one output value. We say "the output is a function of the input."
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1.2: Domain and Range
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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.
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1.3: Rates of Change and Behavior of Graphs
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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.
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1.4: Composition of Functions
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When the output of one function is used as the input of another, we call the entire operation a composition of functions.
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1.5: Transformation of Functions
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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.
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1.6: Inverse Functions
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